Exhibit 23.2

Consent of Independent Registered Public Accounting Firm

We consent to the incorporation by reference in the Registration Statement (Form S-8) pertaining to the Amended and Restated 2006 Stock Option and Grant Plan and the 2014 Stock Incentive Plan of Concert Pharmaceuticals, Inc. of our report dated March 31, 2014, with respect to the consolidated financial statements of Concert Pharmaceuticals, Inc. included in its Annual Report (Form 10-K) for the year ended December 31, 2013, filed with the Securities and Exchange Commission.

/s/ Ernst & Young LLP

Boston, Massachusetts

April 4, 2014