Net Loss Per Share - Calculation of Basic and Diluted Net Loss per Share (Details) - USD ($) $ / shares in Units, $ in Thousands	3 Months Ended
	Mar. 31, 2021	Mar. 31, 2020
Numerator:
Net loss	$ (265,328)	$ (172,937)
Net loss attributable to non-controlling interests	(360)	0
Net loss attributable to Biohaven Pharmaceutical Holding Company Ltd.	$ (264,968)	$ (172,937)
Denominator:
Weighted average common shares outstanding - basic (shares)	62,040,715	56,412,439
Weighted average common shares outstanding - diluted (shares)	62,040,715	56,412,439
Net loss per share attributable to common shareholders of Biohaven Pharmaceutical Holding Company Ltd. - basic (in dollars per share)	$ (4.27)	$ (3.07)
Net loss per share attributable to common shareholders of Biohaven Pharmaceutical Holding Company Ltd. - diluted (in dollars per share)	$ (4.27)	$ (3.07)