EX-99.(a)(1)(D)

THE OFFER AND WITHDRAWAL RIGHTS WILL EXPIRE AT 12:00 MIDNIGHT, NEW YORK CITY TIME, ON APRIL 21, 2016 (ONE MINUTE AFTER 11:59 P.M. NEW YORK CITY TIME ON APRIL 21, 2016), UNLESS THE OFFER IS EXTENDED.

We have been engaged by Pomegranate Merger Sub, Inc., a Delaware corporation (the “Offeror”) and a wholly owned subsidiary of Pomegranate Holdings, Inc., a Delaware corporation (“Parent”), to act as information agent (“Information Agent”) in connection with the Offeror’s offer to purchase all of the issued and outstanding shares of common stock, par value $0.01 per share (the “Shares”), of The Fresh Market, Inc., a Delaware corporation (“The Fresh Market”), at a purchase price of $28.50 per Share, net to the holders thereof, payable in cash, without interest, less any applicable tax withholding, upon the terms and subject to the conditions set forth in the Offer to Purchase, dated March 25, 2016 (the “Offer to Purchase”), and in the related Letter of Transmittal (the “Letter of Transmittal” which, together with the Offer to Purchase, as each may be amended or supplemented from time to time as permitted under the Merger Agreement described below, collectively constitute the “Offer”). Parent and the Offeror are controlled by certain equity funds managed by Apollo Management VIII, L.P. Please furnish copies of the enclosed materials to those of your clients for whom you hold Shares registered in your name or in the name of your nominee.

The Offer is not subject to any financing condition. The Offer is subject to the conditions described in Section 13—“Conditions of the Offer” of the Offer to Purchase.

For your information and for forwarding to your clients for whom you hold Shares registered in your name or in the name of your nominee, we are enclosing the following documents:

2. the Letter of Transmittal to be used by stockholders of The Fresh Market in accepting the Offer and tendering Shares, including Guidelines for Certification of Taxpayer Identification Number on Substitute Form W-9;

3. the Notice of Guaranteed Delivery to be used to accept the Offer if Shares to be tendered and/or all other required documents cannot be delivered to American Stock Transfer & Trust Company, LLC (the “Depositary and Paying Agent”) by the expiration of the Offer or if the procedure for book-entry transfer cannot be completed by the expiration of the Offer;

4. The Fresh Market’s Solicitation/Recommendation Statement on Schedule 14D-9;

5. the form of letter that may be sent to your clients for whose accounts you hold Shares in your name or in the name of your nominee, with space provided for obtaining such clients’ instructions with regard to the Offer; and

6. the return envelope addressed to the Depositary and Paying Agent for your use only.

Certain conditions to the Offer are described in Section 13—“Conditions of the Offer” of the Offer to Purchase.

Your prompt action is requested. We urge you to contact your clients as promptly as possible. Please note that the Offer will expire at 12:00 midnight, New York City time, on April 21, 2016 (one minute after 11:59 P.M. New York City time on April 21, 2016), unless the Offer is extended. Previously tendered Shares may be withdrawn at any time until the Offer has expired; and, if not previously accepted for payment at any time, after May 24, 2016, pursuant to SEC (as defined in the Offer to Purchase) regulations.

The Offer is being made pursuant to the Agreement and Plan of Merger, dated as of March 11, 2016, by and among The Fresh Market, Parent and the Offeror (as it may be amended from time to time, the “Merger Agreement”), pursuant to which, after completion of the Offer and the satisfaction or waiver of certain conditions set forth therein, the Offeror has agreed to merge with and into The Fresh Market, with The Fresh Market surviving as a wholly owned subsidiary of Parent (the “Merger”). Parent and the Offeror are controlled by certain equity funds managed by Apollo Management VIII, L.P.

The Fresh Market Board has (a) determined that the Offer, the Merger and the other transactions contemplated by the Merger Agreement, but excluding, in any event, the related financing (the “Transactions”), are fair to and in the best interests of The Fresh Market and its stockholders (other than the holders of the Rollover Shares (as defined in the Offer to Purchase)), (b) declared the Merger Agreement and the Transactions advisable and (c) recommended that The Fresh Market’s stockholders tender their Shares in the Offer.

For Shares to be validly tendered pursuant to the Offer, (a) the share certificates or confirmation of receipt of such Shares under the procedure for book-entry transfer, together with a properly completed and duly executed Letter of Transmittal, including any required medallion signature guarantees, or an “Agent’s Message” (as defined in Section 3—“Procedures for Tendering Shares” of the Offer to Purchase) in the case of book-entry transfer, and any other documents required in the Letter of Transmittal, must be timely received by the Depositary and Paying Agent or (b) the tendering stockholder must comply with the guaranteed delivery procedures, all in accordance with the Offer to Purchase and the Letter of Transmittal.

Neither Parent nor the Offeror will pay any fees or commissions to any broker or dealer or other person (other than the Information Agent and the Depositary and Paying Agent, as described in the Offer to Purchase)

for soliciting tenders of Shares pursuant to the Offer. The Offeror will, however, upon request, reimburse brokers, dealers, commercial banks, trust companies and other nominees for reasonable and necessary costs and expenses incurred by them in forwarding materials to their customers. The Offeror will pay all stock transfer taxes applicable to its purchase of Shares pursuant to the Offer, subject to Instruction 6 of the Letter of Transmittal.

The Offer is not being made to, nor will tenders be accepted from or on behalf of, holders of Shares in any jurisdiction in which the making of the Offer or acceptance thereof would not be in compliance with the securities, “blue sky” or other laws of such jurisdiction.

Questions and requests for assistance or for additional copies of the enclosed materials may be directed to the Information Agent, at the address and telephone number set forth in the Offer to Purchase. Additional copies of the enclosed materials will be furnished at the Offeror’s expense.

NOTHING CONTAINED HEREIN OR IN THE ENCLOSED DOCUMENTS SHALL RENDER YOU OR ANY PERSON THE AGENT OF PARENT, THE OFFEROR, THE FRESH MARKET, THE INFORMATION AGENT, THE DEPOSITARY AND PAYING AGENT, OR ANY OF THEIR AFFILIATES, OR AUTHORIZE YOU OR ANY OTHER PERSON TO USE ANY DOCUMENT OR MAKE ANY STATEMENT OR REPRESENTATION ON BEHALF OF ANY OF THEM WITH RESPECT TO THE OFFER NOT CONTAINED IN THE OFFER TO PURCHASE OR THE LETTER OF TRANSMITTAL.