Exhibit 5.1

Proskauer Rose LLP Eleven Times Square, New York, New York 10036-8299

June 17, 2024

Shake Shack Inc.

225 Varick Street

Suite 301

New York, New York 10014

Ladies and Gentlemen:

We are acting as counsel to Shake Shack Inc., a Delaware corporation (the “Company”), in connection with the preparation and filing with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Securities Act”), of a registration statement on Form S-8 (the “Registration Statement”), relating to the registration of an additional 842,321 shares of Class A Common Stock, par value $0.001 per share (the “Shares”), that may be issued by the Company pursuant to the Shake Shack Inc. 2025 Incentive Award Plan, as amended and restated and amended from time to time (the “Plan”).

As such counsel, we have participated in the preparation of the Registration Statement and have examined originals or copies of such documents, corporate records and other instruments as we have deemed relevant, including, without limitation: (i) the Company’s Amended and Restated Certificate of Incorporation; (ii) the Company’s Second Amended and Restated Bylaws; (iii) certain of the resolutions of the Board of Directors of the Company relating to the Plan and to the authorization for the issuance of the Shares; and (iv) the Registration Statement, together with the exhibits filed as a part thereof and including any documents incorporated by reference therein.

We have made such examination of law as we have deemed necessary to express the opinion contained herein. As to matters of fact relevant to this opinion, we have relied upon, and assumed without independent verification, the accuracy of certificates of public officials and officers of the Company. We have assumed the genuineness of all signatures, the legal capacity of natural persons, the authenticity of documents submitted to us as originals, the conformity to the original documents of all documents submitted to us as certified, facsimile or photostatic copies, and the authenticity of the originals of such copies.

Based upon the foregoing, and subject to the limitations, qualifications, exceptions and assumptions expressed herein, we are of the opinion, assuming no change in the applicable law or pertinent facts, that when and to the extent the Shares are issued in accordance with the terms of the Plan the Shares will be validly issued, fully paid and non-assessable.

This opinion is based upon and expressly limited in all respects to the General Corporation Law of the State of Delaware, as in effect on the date hereof.

This opinion is expressly limited to the matters set forth above and we render no opinion, whether by implication or otherwise, as to any other matters. This opinion is rendered as of the date hereof, and we disclaim any obligation to advise you of any changes in applicable law or any other facts, circumstances, events, developments or other matters that may come to our attention after the date hereof that may alter, affect or modify the opinion expressed herein.

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We hereby consent to the filing of this opinion letter as Exhibit 5.1 to the Registration Statement. In giving the foregoing consent, we do not admit that we are in the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations of the Commission promulgated thereunder.

Very truly yours,

/s/ Proskauer Rose LLP