The 23-year-old scored the winner against Sunderland on Sunday but was carried off in the 87th minute after turning his ankle while tackling Papy Djilobodji.
"He has injured his ankle ligaments. We will continue to assess him every day but don't want to put a time frame on it," Spurs manager Mauricio Pochettino said on the club's Twitter feed.
Tottenham are third in the league standings, with three wins from five games, and travel to promoted Middlesbrough on Saturday.
They are also competing in the Champions League again after a five-year absence, with group-stage matches against CSKA Moscow and Bayer Leverkusen on Sept. 27 and Oct. 18.
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A prolonged absence for Kane could also hit England, who have a World Cup qualifier against Scotland at Wembley on Nov. 11.
Kane ended last season as the Premier League's top scorer with 25 goals, the first Englishman to achieve the feat since Sunderland's Kevin Phillips in 1999-2000.
(Reporting by Alan Baldwin, editing by Ed Osmond)
