Exhibit (17)(d)

[LOGO]

OFFER TO EXCHANGE

$175,000,000 AGGREGATE PRINCIPAL AMOUNT OF

SERIES HH FLOATING RATE SENIOR NOTES DUE AUGUST 19, 2016

FOR

$175,000,000 AGGREGATE PRINCIPAL AMOUNT OF

SERIES HH FLOATING RATE SENIOR NOTES DUE AUGUST 19, 2016

THAT HAVE BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933,

AS AMENDED, PURSUANT TO THE PROSPECTUS, DATED             , 2013

To: Brokers, Dealers, Commercial Banks,

Trust Companies and Other Nominees

Kayne Anderson MLP Investment Company, a Maryland corporation (the “Company”) is offering, upon and subject to the terms and conditions set forth in the Prospectus, dated             , 2013 (the “Prospectus”), and the enclosed Letter of Transmittal (the “Letter of Transmittal”), to exchange (the “Exchange Offer”) its issued and outstanding Series HH Floating Rate Senior Notes due August 19, 2016 (the “Old Notes”) for its Series HH Floating Rate Senior Notes due August 19, 2016 that have been registered under the Securities Act of 1933, as amended. The Exchange Offer is being made in order to satisfy certain obligations of the Company contained in the Registration Rights Agreement, dated as of August 22, 2013, among the Company, as issuer, and the initial purchaser of the Old Notes resulting in the issuance of the Old Notes.

We are requesting that you contact your clients for whom you hold Old Notes regarding the Exchange Offer. For your information and for forwarding to your clients for whom you hold Old Notes registered in your name or in the name of your nominee, or who hold Old Notes registered in their own names, we are enclosing the following documents:

1. Prospectus, dated             , 2013;

2. The Letter of Transmittal for your use and for the information of your clients;

3. A form of letter which may be sent to your clients for whose account you hold Old Notes registered in your name or the name of your nominee, with space provided for obtaining such clients’ instructions with regard to the Exchange Offer; and

4. Return envelopes addressed to The Bank of New York Mellon, N.A., the Exchange Agent for the Exchange Offer.

YOUR PROMPT ACTION IS REQUESTED. THE EXCHANGE OFFER WILL EXPIRE AT 5:00 P.M., NEW YORK CITY TIME, ON             , 2014, UNLESS EXTENDED BY THE COMPANY (THE “EXPIRATION DATE”). OLD NOTES TENDERED PURSUANT TO THE EXCHANGE OFFER MAY BE WITHDRAWN AT ANY TIME PRIOR TO 5:00 P.M., NEW YORK CITY TIME, ON THE EXPIRATION DATE.

To participate in the Exchange Offer, a duly executed and properly completed Letter of Transmittal (or facsimile thereof or Agent’s Message in lieu thereof), with any required signature guarantees and any other required documents, should be sent to the Exchange Agent, and certificates representing the Old Notes should be delivered to the Exchange Agent, all in accordance with the instructions set forth in the Letter of Transmittal and the Prospectus.

The Company will, upon request, reimburse brokers, dealers, commercial banks and trust companies for reasonable and necessary costs and expenses incurred by them in forwarding the Prospectus and the related documents to the beneficial owners of Old Notes held by them as nominee or in a fiduciary capacity. The Company will pay or cause to be paid all stock transfer taxes applicable to the exchange of Old Notes pursuant to the Exchange Offer, except as set forth in Instruction 5 of the Letter of Transmittal.

Any inquiries you may have with respect to the Exchange Offer, or requests for additional copies of the enclosed materials, should be directed to The Bank of New York Mellon, Trust Company, N.A., the Exchange Agent for the Exchange Offer, at its address and telephone number set forth on the front of the Letter of Transmittal.

Very truly yours,

Kayne Anderson MLP Investment Company

NOTHING HEREIN OR IN THE ENCLOSED DOCUMENTS SHALL CONSTITUTE YOU OR ANY PERSON AS AN AGENT OF THE COMPANY OR THE EXCHANGE AGENT, OR AUTHORIZE YOU OR ANY OTHER PERSON TO USE ANY DOCUMENT OR MAKE ANY STATEMENTS ON BEHALF OF EITHER OF THEM WITH RESPECT TO THE EXCHANGE OFFER, EXCEPT FOR STATEMENTS EXPRESSLY MADE IN THE PROSPECTUS OR THE LETTER OF TRANSMITTAL.

Enclosures