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

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 March 15, 2019,
to shareholders of record as of March 4, 2019. The ex-dividend date is
expected to be March 1, 2019. 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 2019 distributions will be made after
the end of 2019 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, YieldCos, 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 (collectively, "Energy Infrastructure
Companies"). To generate additional income, the Fund expects to write
(or sell) covered call options on up to 35% of the managed assets held
in the Fund's portfolio.

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 $121 billion as of January 31, 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 January 31, 2019,
EIP managed or supervised approximately $5.9 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 prospectus,
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 and the Internal Revenue
Code. First Trust has no knowledge of and has not been provided any
information regarding any investor. Financial advisors must determine
whether particular investments are appropriate for their clients. First
Trust believes the financial advisor is a fiduciary, is capable of
evaluating investment risks independently and is responsible for
exercising independent judgment with respect to its retirement plan
clients.

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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