Cue Biopharma, Inc.

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. )

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☒ Definitive Proxy Statement

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Cue Biopharma, Inc.

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40 Guest Street

Boston, Massachusetts 02135

NOTICE OF 2026 ANNUAL MEETING OF STOCKHOLDERS

To Be Held on Monday, April 13, 2026

Dear Stockholder:

You are cordially invited to the 2026 Annual Meeting of Stockholders, or the Annual Meeting, of Cue Biopharma, Inc. The Annual Meeting will be held exclusively via the Internet in a virtual meeting format atwww.virtualshareholdermeeting.com/CUE2026 on Monday, April 13, 2026 at 9:00 a.m. Eastern Time. The stockholders will consider and vote on the following matters:

The election of seven nominees to our board of directors (Proposal 1);

The ratification of the appointment of RSM US LLP as our independent registered public accounting firm for the fiscal year ending December 31, 2026 (Proposal 2);

The approval, on a non-binding advisory basis, of the compensation of our named executive officers (Proposal 3);

The adoption and approval of an amendment to our Amended and Restated Certificate of Incorporation, as amended, to effect a reverse stock split of our issued shares of common stock at a ratio within the range of not less than 1-for-30 and not more than 1-for-50, with the exact ratio within such range and the implementation and timing of such reverse stock split to be determined at the sole discretion of our board of directors without further approval or authorization of our stockholders (Proposal 4); and

The transaction of any other business that may properly come before the Annual Meeting or any adjournment or postponement thereof.

Our stockholders of record as of the close of business on March 9, 2026, or the record date, are entitled to participate in and vote at the Annual Meeting. To participate in the Annual Meeting, including to vote and ask questions, stockholders of record should go to the meeting website at www.virtualshareholdermeeting.com/CUE2026, enter the 16-digit control number found on your proxy card or voting instruction form and follow the instructions on the website.

A printed copy of our proxy materials, including this Proxy Statement, our 2025 Annual Report to Stockholders, which includes our Annual Report on Form 10-K for the fiscal year ended December 31, 2025, and a proxy card, is being mailed to our stockholders on or about March 16, 2026 and sent by email to our stockholders who have opted for such means of delivery on or about March 16, 2026.

We encourage all stockholders to attend the Annual Meeting online. However, whether or not you plan to attend the Annual Meeting online, we encourage you to read the Proxy Statement and submit your proxy or voting instructions as soon as possible. Please review the instructions on how to vote your shares online during the Annual Meeting as described in the Proxy Statement.

By the Order of the Board of Directors,

/s/ Colin Sandercock

Colin Sandercock

Senior Vice President, General Counsel and Secretary

Boston, Massachusetts

March 16, 2026

Important Notice Regarding the Availability of Proxy Materials for the 2026 Annual Meeting of Stockholders to be Held on April 13, 2026: You will be able to view this Proxy Statement, our 2025 Annual Report to Stockholders, which includes our Annual Report on Form 10-K for the fiscal year ended December 31, 2025, and a proxy card or voting instruction form online at www.proxyvote.com.