EXHIBIT 23.1

CONSENT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

We consent to the incorporation by reference in the Registration Statement (Form S-8) pertaining to the 2017 Equity Incentive Plan and 2017 Employee Share Purchase Plan of Biohaven Pharmaceutical Holding Company Ltd., of our reports dated March 1, 2021, with respect to the consolidated financial statements of Biohaven Pharmaceutical Holding Company Ltd. and the effectiveness of internal control over financial reporting of Biohaven Pharmaceutical Holding Company Ltd. included in its Annual Report (Form 10-K) for the year ended December 31, 2020, filed with the Securities and Exchange Commission.

/s/ Ernst & Young, LLP

Hartford, Connecticut

March 1, 2021