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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 Biohaven Pharmaceutical Holding Company Ltd. for the registration of 115,836 shares of its common shares and to the incorporation by reference therein 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