Exhibit 5.1

Goodwin Procter LLP 100 Northern Avenue Boston, MA 02210   goodwinlaw.com +1 617 570 1000

November 9, 2022

TScan Therapeutics, Inc.

830 Winter Street

Waltham, MA 02451

Re: Securities Registered under Registration Statement on Form S-3

We have acted as counsel to you in connection with your filing of a Registration Statement on Form S-3 (as amended or supplemented, the “Registration Statement”) on November 9, 2022, with the Securities and Exchange Commission pursuant to the Securities Act of 1933, as amended (the “Securities Act”), relating to the registration by TScan Therapeutics, Inc., a Delaware corporation (the “Company”), of the offer and sale, from time to time, by the selling stockholders listed in the Registration Statement under “Selling Stockholders,” of up to 7,061,380 shares (the “Shares”) of the Company’s common stock, $0.0001 par value per share.

We have reviewed such documents and made such examination of law as we have deemed appropriate to give the opinions set forth below. We have relied, without independent verification, on certificates of public officials and, as to matters of fact material to the opinions set forth below, on certificates of officers of the Company.

The opinion set forth below is limited to the General Corporation Law of the State of Delaware.

Based on the foregoing, we are of the opinion that the Shares have been duly authorized and validly issued and are fully paid and non-assessable.

We hereby consent to the inclusion of this opinion as Exhibit 5.1 to the Registration Statement and to the reference to our firm under the caption “Legal Matters” in the Registration Statement. In giving our 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 thereunder.

Very truly yours,

/s/ Goodwin Procter LLP

GOODWIN PROCTER LLP