The Board of Trustees of First Trust Energy Infrastructure Fund (the "Fund") (NYSE:FIF), CUSIP 33738C103, previously approved a managed distribution policy for the Fund (the "Managed Distribution Plan") in reliance on exemptive relief received from the Securities and Exchange Commission which permits the Fund to make periodic distributions of long-term capital gains as frequently as monthly each tax year.

The Fund has declared a distribution payable on June 15, 2023, to shareholders of record as of June 2, 2023, with an ex-dividend date of June 1, 2023. This Notice is meant to provide you information about the sources of your Fund's distributions. You should not draw any conclusions about the Fund's investment performance from the amount of its distribution or from the terms of its Managed Distribution Plan.

The following tables set forth the estimated amounts of the current distribution and the cumulative distributions paid this fiscal year to date for the Fund from the following sources: net investment income ("NII"); net realized short-term capital gains ("STCG"); net realized long-term capital gains ("LTCG"); and return of capital ("ROC"). These estimates are based upon information as of May 31, 2023, are calculated based on a generally accepted accounting principles ("GAAP") basis and include the prior fiscal year-end undistributed net investment income. The amounts and sources of distributions are expressed per common share.

5 Yr. Avg.

Annualized Current

Annual Total

Fund

Fiscal

Total Current

Current Distribution ($)

Current Distribution (%)

Dist. Rate as a

Return

Ticker

Cusip

Year End

Distribution

NII

STCG

LTCG

ROC ⁽²⁾

NII

STCG

LTCG

ROC⁽²⁾

% of NAV⁽³⁾

on NAV⁽⁴⁾

FIF⁽⁵⁾

33738C103

11/30/2023

$0.10000

100.00%

7.40%

6.60%

Total

Cumulative

Cumulative Fiscal

Fund

Fiscal

Cumulative Fiscal YTD

Cumulative Distributions Fiscal YTD ($)

Cumulative Distributions Fiscal YTD (%)

Fiscal YTD Distributions as

YTD Total Return

Ticker

Cusip

Year End

Distributions⁽¹⁾

NII

STCG

LTCG

ROC ⁽²⁾

NII

STCG

LTCG

ROC⁽²⁾

a % of NAV⁽³⁾

on NAV⁽⁴⁾

FIF⁽⁵⁾

33738C103

11/30/2023

$0.55900

100.00%

3.45%

-6.73%

(1) Includes the most recent monthly distribution paid on June 15, 2023.

(2) The Fund estimates that it has distributed more than its income and net realized capital gains; therefore, a portion of your distribution may be a return of capital. A return of capital may occur, for example, when some or all of the money that you invested in the Fund is paid back to you. A return of capital distribution does not necessarily reflect the Fund's investment performance and should not be confused with "yield" or "income."

(3) Based on Net Asset Value ("NAV") as of May 31, 2023.

(4) Total Returns are through May 31, 2023.

(5) The Fund anticipates that, due to the tax treatment of cash distributions made by Master Limited Partnerships in which the Fund invests, a portion of distributions the Fund makes to Common Shareholders may consist of a tax-deferred return of capital.

The amounts and sources of distributions reported in this Notice are only estimates and are not being provided for tax reporting purposes. The actual amounts and sources of the amounts for tax reporting purposes will depend upon the Fund's investment experience during the remainder of its fiscal year and may be subject to changes based on tax regulations. The Fund will send you a Form 1099-DIV for the calendar year that will tell you how to report these distributions for federal income tax purposes. You should not use this Notice as a substitute for your Form 1099-DIV.

First Trust Advisors L.P. ("FTA") is a federally registered investment advisor and serves as the Fund's investment advisor. FTA and its affiliate First Trust Portfolios L.P. ("FTP"), a FINRA registered broker-dealer, are privately-held companies that provide a variety of investment services. FTA has collective assets under management or supervision of approximately $190 billion as of May 31, 2023 through unit investment trusts, exchange-traded funds, closed-end funds, mutual funds and separate managed accounts. FTA is the supervisor of the First Trust unit investment trusts, while FTP is the sponsor. FTP is also a distributor of mutual fund shares and exchange-traded fund creation units. FTA and FTP are based in Wheaton, Illinois.

Energy Income Partners, LLC ("EIP") serves as the Fund's investment sub-advisor and provides advisory services to a number of investment companies and partnerships for the purpose of investing in MLPs and other energy infrastructure securities. EIP is one of the early investment advisors specializing in this area. As of May 31, 2023, EIP managed or supervised approximately $5.0 billion in client assets.

Principal Risk Factors: Risks are inherent in all investing. Certain risks applicable to the Fund are identified below, which includes the risk that you could lose some or all of your investment in the Fund. The principal risks of investing in the Fund are spelled out in the Fund's annual shareholder reports. The order of the below risk factors does not indicate the significance of any particular risk factor. The Fund also files reports, proxy statements and other information that is available for review.

Past performance is no assurance of future results. Investment return and market value of an investment in the Fund will fluctuate. Shares, when sold, may be worth more or less than their original cost. There can be no assurance that the Fund's investment objectives will be achieved. The Fund may not be appropriate for all investors.

The Fund is subject to risks, including the fact that it is a non-diversified closed-end management investment company.

Securities held by a fund, as well as shares of a fund itself, are subject to market fluctuations caused by factors such as general economic conditions, political events, regulatory or market developments, changes in interest rates and perceived trends in securities prices. Shares of a fund could decline in value or underperform other investments as a result of the risk of loss associated with these market fluctuations. In addition, local, regional or global events such as war, acts of terrorism, spread of infectious diseases or other public health issues, recessions, natural disasters or other events could have a significant negative impact on a fund and its investments. Such events may affect certain geographic regions, countries, sectors and industries more significantly than others. In February 2022, Russia invaded Ukraine which has caused and could continue to cause significant market disruptions and volatility within the markets in Russia, Europe, and the United States. The hostilities and sanctions resulting from those hostilities could have a significant impact on certain fund investments as well as fund performance. The COVID-19 global pandemic and the ensuing policies enacted by governments and central banks have caused and may continue to cause significant volatility and uncertainty in global financial markets. While vaccines have been developed, there is no guarantee that vaccines will be effective against future variants of the disease. Recent and potential future bank failures could result in disruption to the broader banking industry or markets generally and reduce confidence in financial institutions and the economy as a whole, which may also heighten market volatility and reduce liquidity.

Because the Fund is concentrated in securities issued by energy infrastructure companies, it will be more susceptible to adverse economic or regulatory occurrences affecting that industry, including high interest costs, high leverage costs, the effects of economic slowdown, surplus capacity, increased competition, uncertainties concerning the availability of fuel at reasonable prices, the effects of energy conservation policies and other factors. Investments in securities of MLPs involve certain risks different from or in addition to the risks of investing in common stocks. The number of energy-related MLPs has declined since 2014. The industry is witnessing the consolidation or simplification of corporate structures where the MLP sleeve of capital is being eliminated. As a result of the foregoing, the Fund's MLP investments could become less diverse and the Fund may increase its non-MLP investments consistent with its investment objective and policies. Changes in tax laws or regulations, or interpretations thereof in the future, could adversely affect the Fund or the MLPs, MLP-related entities and other energy sector and energy utility companies in which the Fund invests.

The Fund invests in securities of non-U.S. issuers which are subject to higher volatility than securities of U.S. issuers. Because the Fund invests in non-U.S. securities, you may lose money if the local currency of a non-U.S. market depreciates against the U.S. dollar.

There can be no assurance as to what portion of the distributions paid to the Fund's Common Shareholders will consist of tax-advantaged qualified dividend income.

To the extent a fund invests in floating or variable rate obligations that use the London Interbank Offered Rate ("LIBOR") as a reference interest rate, it is subject to LIBOR Risk. The United Kingdom's Financial Conduct Authority, which regulates LIBOR has ceased making LIBOR available as a reference rate over a phase-out period that began December 31, 2021. There is no assurance that any alternative reference rate, including the Secured Overnight Financing Rate ("SOFR") will be similar to or produce the same value or economic equivalence as LIBOR or that instruments using an alternative rate will have the same volume or liquidity. The unavailability or replacement of LIBOR may affect the value, liquidity or return on certain fund investments and may result in costs incurred in connection with closing out positions and entering into new trades. Any potential effects of the transition away from LIBOR on the fund or on certain instruments in which the fund invests can be difficult to ascertain, and they may vary depending on a variety of factors, and they could result in losses to the fund.

Use of leverage can result in additional risk and cost, and can magnify the effect of any losses.

The risks of investing in the Fund are spelled out in the shareholder reports and other regulatory filings.

The information presented is not intended to constitute an investment recommendation for, or advice to, any specific person. By providing this information, First Trust is not undertaking to give advice in any fiduciary capacity within the meaning of ERISA, the Internal Revenue Code or any other regulatory framework. Financial professionals are responsible for evaluating investment risks independently and for exercising independent judgment in determining whether investments are appropriate for their clients.

Forward-Looking Statements

Certain statements made in this press release that are not historical facts are referred to as "forward‑looking statements" under the U.S. federal securities laws. Actual future results or occurrences may differ significantly from those anticipated in any forward‑looking statements due to numerous factors. Generally, the words "believe," "expect," "intend," "estimate," "anticipate," "project," "will" and similar expressions identify forward‑looking statements, which generally are not historical in nature. Forward‑looking statements are subject to certain risks and uncertainties that could cause actual results to differ from those anticipated in any forward-looking statements. You should not place undue reliance on forward‑looking statements, which speak only as of the date they are made. The Fund undertakes no responsibility to update publicly or revise any forward‑looking statements.

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First Trust Energy Infrastructure Fund Issues Notice Regarding June 2023 Distribution