The experienced Croatia international, 34, sustained the injury during non-contact training, his club confirmed.
He is set to undergo surgery on his right knee before commencing his rehabilitation in north London.
Perisic joined Tottenham on a two-year deal from Inter Milan in 2022 and his contract is set to expire next July.
Spurs are unbeaten in five Premier League matches under new manager Ange Postecoglou this season, winning four and drawing once to sit second in the table.
Perisic, a Champions League winner with Bayern Munich in 2019-20 and Italian champion with Inter Milan in 2020-21, is unlikely to add to his five substitute appearances so far in the 2023-24 campaign.
