The England international was stretchered off the pitch in the second half of Spurs' 1-0 victory over Sunderland at White Hart Lane on Sunday.
Kane, who scored the only goal of the game, suffered the blow when he twisted his ankle while tackling Papy Djilobodji in the Premier League match.
After the striker underwent a second scan today, manager Mauricio Pochettino confirmed to reporters that Kane has damaged ankle ligaments, but that the club "don't want to put a timeframe" on the 23-year-old's return.
According to numerous reports in the British media, there are fears among the Spurs camp that Kane could be on the treatment table for up to eight weeks.
The forward ended a four-month goalscoring drought for club and country on September 10, netting in back-to-back league games.