First Trust Energy Infrastructure Fund Declares its Monthly Common Share Distribution of $0.11 Per Share for June

First Trust Energy Infrastructure Fund (the "Fund") (NYSE: FIF) has declared the Fund’s regularly scheduled monthly common share distribution in the amount of $0.11 per share payable on June 15, 2017, to shareholders of record as of June 5, 2017. The ex-dividend date is expected to be June 1, 2017. The monthly distribution information for the Fund appears below.

The Fund's Board of Trustees has approved a managed distribution policy for the Fund (the "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. Under the Plan, the Fund intends to continue to pay its recurring monthly distribution in the amount of $0.11 per share that reflects the distributable cash flow of the Fund. A portion of this monthly distribution may include long-term capital gains. This may result in a reduction of the long-term capital gain distribution necessary at year end by distributing long-term capital gains throughout the year. The annual distribution rate is independent of the Fund's performance during any particular period. Accordingly, you should not draw any conclusions about the Fund's investment performance from the amount of any distribution or from the terms of the Plan.

The distribution may consist of net investment income earned by the Fund, net short-term and long-term capital gains and/or tax-deferred return of capital. Tax-deferred return of capital, if any, is primarily due to the tax treatment of cash distributions made by master-limited partnerships ("MLPs") in which the Fund invests. The final determination of the source of tax status of all 2017 distributions will be made after the end of 2017 and will be provided on Form 1099-DIV.

The Fund is a non-diversified, closed-end management investment company that seeks to provide a high level of total return with an emphasis on current distributions paid to shareholders. The Fund seeks to achieve its investment objectives by investing primarily in securities of companies engaged in the energy infrastructure sector. These companies principally include publicly-traded MLPs and limited liability companies taxed as partnerships, MLP affiliates, Canadian income trusts and their successor companies, pipeline companies, utilities, and other companies that derive at least 50% of their revenues from operating or providing services in support of infrastructure assets such as pipelines, power transmission and petroleum and natural gas storage in the petroleum, natural gas and power generation industries. To generate additional income, the Fund expects to write (or sell) covered call options on up to 30% of the managed assets held in the Fund's portfolio.

First Trust Advisors L.P., the Fund's investment advisor, along with its affiliate, First Trust Portfolios L.P., are privately-held companies which provide a variety of investment services, including asset management and financial advisory services, with collective assets under management or supervision of approximately $105 billion as of April 30, 2017 through unit investment trusts, exchange-traded funds, closed-end funds, mutual funds and separate managed accounts.

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 April 30, 2017, EIP managed or supervised approximately $5.8 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.

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 Fund’s daily closing New York Stock Exchange price and net asset value per share as well as other information can be found at www.ftportfolios.com or by calling 1-800-988-5891.

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