First Trust Energy Infrastructure Fund Issues Notice Regarding October 2019 Distribution

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 October 15, 2019, to shareholders of record as of October 2, 2019, with an ex-dividend date of October 1, 2019. 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 September 30, 2019, 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.

^{(1) Includes the most recent monthly distribution paid on October 15, 2019.}

^{(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 September 30, 2019.}

^{(4) Total Returns are through September 30, 2019.}

^{(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 $134 billion as of September 30, 2019 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 September 30, 2019, EIP managed or supervised approximately $6.4 billion in client assets.

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.

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

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.

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.

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 advisors 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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