Concert Pharmaceuticals (CNCE) 10-K 2016 FY Annual report

Exhibit 23.1

Consent of Independent Registered Public Accounting Firm

We consent to the incorporation by reference in the Registration Statement (Form S-3 No. 333-202451) of Concert Pharmaceuticals, Inc. and the related Prospectus, the 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., the Registration Statement (Form S-8 No. 333-202453) pertaining to the 2014 Stock Incentive Plan of Concert Pharmaceuticals, Inc., and the Registration Statement (From S-8 No. 333-209841) pertaining to the 2014 Stock Incentive Plan of Concert Pharmaceuticals, Inc., of our report dated March 6, 2017, with respect to the consolidated financial statements of Concert Pharmaceuticals, Inc. included in this Annual Report (Form 10-K) for the year ended December 31, 2016.

/s/ Ernst & Young LLP

Boston, Massachusetts

March 6, 2017