Concert Pharmaceuticals (CNCE) S-3 Shelf registration

Exhibit 23.1

Consent of Independent Registered Public Accounting Firm

We consent to the reference to our firm under the caption “Experts” in the Registration Statement (Form S-3) and related Prospectus of Concert Pharmaceuticals, Inc. for the registration of $250,000,000 of debt securities, common stock, preferred stock, units and warrants, and to the incorporation by reference therein of our reports dated February 27, 2020, with respect to the consolidated financial statements of Concert Pharmaceuticals, Inc., and the effectiveness of internal control over financial reporting of Concert Pharmaceuticals, Inc., included in its Annual Report (Form 10-K) for the year ended December 31, 2019, filed with the Securities and Exchange Commission.

/s/ Ernst & Young LLP

Boston, Massachusetts

November 5, 2020