UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

WASHINGTON, D.C. 20549

SCHEDULE 14A

Proxy Statement Pursuant to Section 14(a)

of the Securities Exchange Act of 1934

(Amendment No.     )

Filed by the Registrant  ☑                             Filed by a Party other than the Registrant  ☐

Check the appropriate box:

☐	Preliminary Proxy Statement
☐	Confidential, for Use of the Commission Only (as permitted by Rule 14a-6(e)(2))
☐	Definitive Proxy Statement
☐	Definitive Additional Materials
☒	Soliciting Material Pursuant to §240.14a-12

KAYNE ANDERSON ENERGY INFRASTRUCTURE FUND, INC.

(Name of Registrant as Specified In Its Charter)

(Name of Person(s) Filing Proxy Statement, if other than the Registrant)

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KAYNE ANDERSON ENERGY INFRASTRUCTURE FUND NYSE: KYN 811 Main Street, 14th Floor Houston, TX 77002

Dear Valued Stockholder,

Thank you for being an investor in Kayne Anderson Energy Infrastructure Fund (formerly known as Kayne Anderson MLP/Midstream Investment Company). You are a significant KYN shareholder, and your proxy vote is critical. You were recently sent proxy materials for KYN”s upcoming Special Meeting of Stockholders scheduled for October 22, 2020. If you have not yet cast your proxy vote, please do so today. For your convenience, we have enclosed another copy of your proxy card.

At KYN’s Special Meeting, shareholders are being asked to 1) approve an amendment to KYN’s investment objective, and 2) to approve an amendment to KYN’s fundamental investment policy with respect to industry concentration. KYN’s Board of Directors believe the proposed changes are needed to give the Company more flexibility to invest across a full spectrum of North American energy infrastructure. Additional benefits of the proposed changes are detailed in the Proxy Statement. The Board of Directors of KYN unanimously recommends that shareholders vote “FOR” the proposals.

For more information, please refer to the proxy statement, which can be found at www.kaynefunds.com/proxyinformation. If you have any proxy related questions, or would like to cast your proxy vote by phone, please call 1-866-745-0272 for assistance. Representatives are available Monday through Friday 9 a.m. to 10 p.m. ET.

We very much appreciate your attention to this matter. Please help us by casting your vote today.

Sincerely,

James C. Baker

Chairman of the Board of Directors,

President and CEO

How do I vote? There are four convenient methods for casting your important proxy vote:

1. Vote by touch-tone phone: You may cast your vote by telephone using an automated system by calling the toll-free number found on the enclosed proxy card(s).

2. Vote online: You may cast your vote by visiting the web address located on the enclosed proxy card(s) and following the instructions on the website.

KAYNE ANDERSON ENERGY INFRASTRUCTURE FUND NYSE: KYN 811 Main Street, 14th Floor Houston, TX 77002

Dear Valued Stockholder,

Thank you for being an investor in Kayne Anderson Energy Infrastructure Fund (formerly known as Kayne Anderson MLP/Midstream Investment Company). You are a significant KYN shareholder, and your proxy vote is critical. You were recently sent proxy materials for KYN”s upcoming Special Meeting of Stockholders scheduled for October 22, 2020. If you have not yet cast your proxy vote, please do so today. For your convenience, we have enclosed another copy of your proxy card.

At KYN’s Special Meeting, shareholders are being asked to 1) approve an amendment to KYN’s investment objective, and 2) to approve an amendment to KYN’s fundamental investment policy with respect to industry concentration. KYN’s Board of Directors believe the proposed changes are needed to give the Company more flexibility to invest across a full spectrum of North American energy infrastructure. Additional benefits of the proposed changes are detailed in the Proxy Statement. The Board of Directors of KYN unanimously recommends that shareholders vote “FOR” the proposals.

For more information, please refer to the proxy statement, which can be found at www.kaynefunds.com/proxyinformation. If you have any proxy related questions, or would like to cast your proxy vote by phone, please call 1-866-745-0272 for assistance. Representatives are available Monday through Friday 9 a.m. to 10 p.m. ET.

We very much appreciate your attention to this matter. Please help us by casting your vote today.

Sincerely,

James C. Baker

Chairman of the Board of Directors,

President and CEO

How do I vote? There are four convenient methods for casting your important proxy vote:

1. Vote by Phone with a Representative: You may cast your vote by telephone with a proxy representative by calling toll-free 1-866-745-0272.    Representatives are available Monday through Friday 9 a.m. to 10 p.m. ET.

2. Vote by touch-tone phone: You may cast your vote by telephone using an automated system by calling the toll-free number found on the enclosed proxy card(s).

3. Vote online: You may cast your vote by visiting the web address located on the enclosed proxy card(s) and following the instructions on the website.