Exhibit 5.1

Curis, Inc.

128 Spring Street

Building C – Suite 500

Lexington, MA 02421

Ladies and Gentlemen:

This opinion is being furnished to you in connection with (i) the Registration Statement on Form S-3 (File No. 333-224627) (the “Registration Statement”) filed by Curis, Inc., a Delaware corporation (the “Company”), with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Securities Act”), for the registration of, among other things, shares of Common Stock of the Company, par value $0.01 per share, which may be issued from time to time on a delayed or continuous basis pursuant to Rule 415 under the Securities Act for an aggregate initial offering price not to exceed $200,000,000, as set forth in the Registration Statement and the prospectus contained therein (the “Base Prospectus”) and (ii) the prospectus supplement, dated June 11, 2020 (the “Prospectus Supplement” and, together with the Base Prospectus, the “Prospectus”) relating to the issuance and sale pursuant to the Registration Statement of up to 14,000,000 shares of Common Stock (the “Securities”).

The Securities are to be offered and sold by the Company pursuant to a securities purchase agreement dated June 11, 2020 (the “Purchase Agreement”), between the Company and the purchasers named therein, which is being filed with the Commission as Exhibit 10.1 to the Company’s Current Report on Form 8-K, filed on the date hereof.

We are acting as counsel for the Company in connection with the issue and sale by the Company of the Securities. We have examined copies of the Registration Statement and Base Prospectus as filed and Prospectus Supplement to be filed with the Commission. We have also examined and relied upon the Purchase Agreement, minutes of meetings of the stockholders and the Board of Directors of the Company as provided to us by the Company, the Certificate of Incorporation and By-Laws of the Company, each as restated and/or amended to date, and such other documents as we have deemed necessary for purposes of rendering the opinions hereinafter set forth.

Curis, Inc.

June 11, 2020

Page 2

In our examination of the foregoing documents, we have assumed the genuineness of all signatures, the authenticity of all documents submitted to us as originals, the conformity to original documents of all documents submitted to us as copies, the authenticity of the originals of such latter documents and the legal competence of all signatories to such documents.

We express no opinion herein as to the laws of any state or jurisdiction other than the state laws of the Commonwealth of Massachusetts, the General Corporation Law of the State of Delaware and the federal laws of the United States of America.

Based upon and subject to the foregoing, we are of the opinion that:

Please note that we are opining only as to the matters expressly set forth herein, and no opinion should be inferred as to any other matters. This opinion is based upon currently existing statutes, rules, regulations and judicial decisions, and we disclaim any obligation to advise you of any change in any of these sources of law or subsequent legal or factual developments which might affect any matters or opinions set forth herein.

We hereby consent to the filing of this opinion with the Commission, in accordance with the requirements of Item 601(b)(5) of Regulation S-K under the Securities Act, as an exhibit to the Current Report on Form 8-K to be filed by the Company on the date hereof in connection with the issuance and sale of the Securities and to the use of our name therein and in the related Prospectus Supplement under the caption “Legal Matters.” In giving such consent, we do not hereby 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.

Sincerely,