Exhibit 23.1

Consent of Independent Registered Public Accounting Firm

We consent to the incorporation by reference in the following Registration Statements:

(1)Registration Statement (Form S-3 No. 333-249862) of Concert Pharmaceuticals, Inc. and the related Prospectus;

(2)Registration Statement (Form S-8 No. 333-195125) pertaining to the Amended and Restated 2006 Stock Option and Grant Plan and 2014 Stock Incentive Plan of Concert Pharmaceuticals, Inc.;

(3)Registration Statement (Form S-8 No. 333-202453) pertaining to the 2014 Stock Incentive Plan of Concert Pharmaceuticals, Inc.;

(4)Registration Statement (Form S-8 No. 333-209841) pertaining to the 2014 Stock Incentive Plan of Concert Pharmaceuticals, Inc.;

(5)Registration Statement (Form S-8 No. 333-216459) pertaining to the 2014 Stock Incentive Plan of Concert Pharmaceuticals, Inc.;

(6)Registration Statement (Form S-8 No. 333-223335) pertaining to the 2014 Stock Incentive Plan of Concert Pharmaceuticals, Inc.;

(7)Registration Statement (Form S-8 No. 333-229932) pertaining to the 2014 Stock Incentive Plan of Concert Pharmaceuticals, Inc.;

(8)Registration Statement (Form S-8 No. 333-236679) pertaining to the 2014 Stock Incentive Plan of Concert Pharmaceuticals, Inc.; and

(9)Registration Statement (Form S-8 No. 333-253481) pertaining to the 2014 Stock Incentive Plan of Concert Pharmaceuticals, Inc.;

of our report dated March 3, 2022, with respect to the consolidated financial statements of Concert Pharmaceuticals, Inc. included in this Annual Report (Form 10-K) of Concert Pharmaceuticals, Inc. for the year ended December 31, 2021.

/s/ Ernst & Young LLP

Boston, Massachusetts

March 3, 2022