The 23-year-old is expected to return for the visit of Manchester City on April 21, with Aaron Lennon and William Gallas also set to miss games against Everton and Basel.
The Welshman left White Hart Lane on a stretcher on Thursday night after his right ankle buckled under an innocuous-looking challenge from David Degen, moments before the end of an enthralling Europa League quarterfinal first leg.
The North London club, which currently sits in third in the Premier League table, faces a crucial couple of weeks in its pursuit of Champions League qualification with a clash with sixth-placed Everton on Sunday.
Bale is expected to miss the the weekend game, along with the return leg against Basel the following Thursday before being scheduled to return ahead of the visit of Premier League champions Manchester City on April 21.
Aaron Lennon and William Gallas also limped out for the clash against the Swiss side - that saw Tottenham comes from two goals down to draw level - and the club also confirmed the pair should be fit to face City.