Exhibit 5.1

Yvan-Claude Pierre

+1 212 479 6721

ypierre@cooley.com

April 21, 2020

Shake Shack Inc.

225 Varick Street

Suite 301

New York, New York 10014

Ladies and Gentlemen:

We have represented Shake Shack Inc., a Delaware corporation (the “Company”), in connection with the offering by the Company of 3,416,070 shares, of the Company’s Class A common stock, par value $0.001 per share (the “Shares”), pursuant to a Registration Statement on Form S-3 (File No. 333-225528) the “Registration Statement”), filed with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Act”), the prospectus included within the Registration Statement (the “Base Prospectus”), and the prospectus supplement dated April 17, 2020, filed with the Commission pursuant to Rule 424(b) of the Rules and Regulations of the Act (together with the Base Prospectus, the “Prospectus”).

In connection with this opinion, we have examined and relied upon the Registration Statement, the Prospectus, the Company’s Amended and Restated Certificate of Incorporation, as amended, the Company’s Second Amended and Restated Bylaws, each as currently in effect, and the originals or copies certified to our satisfaction of such records, documents, certificates, memoranda and other instruments as in our judgment are necessary or appropriate to enable us to render the opinion expressed below. We have assumed the genuineness and authenticity of all documents submitted to us as originals, and the conformity to originals of all documents submitted to us as copies thereof, the accuracy, completeness and authenticity of certificates of public officials; and the due authorization, execution and delivery of all documents by all persons other than the Company where authorization, execution and delivery are a prerequisite to the effectiveness thereto. As to certain factual matters, we have relied upon a certificate of an officer of the Company and have not independently verified such matters.

Our opinion herein is expressed solely with respect to the DGCL. We express no opinion to the extent that any other laws are applicable to the subject matter hereof and express no opinion and provide no assurance as to compliance with any federal or state securities law, rule or regulation.

On the basis of the foregoing, and in reliance thereon, we are of the opinion that the Shares, when issued and paid for in accordance with the Underwriting Agreement and as provided in the Prospectus, will be validly issued, fully paid and nonassessable.

We consent to the reference to our firm under the caption “Legal Matters” in the Prospectus and to the filing of this opinion as an exhibit to a Current Report on Form 8-K to be filed with the Commission for incorporation by reference into the Registration Statement. This opinion is expressed as of the date hereof, and we disclaim any responsibility to advise you of any changes in the facts stated or assumed herein or any changes in applicable law.

55 Hudson Yards, New York, NY 10001

T: (212) 479-6000 F: (212) 479-6275 www.cooley.com

April 21, 2020

Page Two

Sincerely,

Cooley LLP

55 Hudson Yards, New York, NY 10001

T: (212) 479-6000 F: (212) 479-6275 www.cooley.com