England international Kane, the Premier League's joint top scorer with 19 goals, hobbled off early at White Hart Lane and there were initial fears that his season could be over.
He missed seven weeks earlier in the season after injuring the same ankle in a Premier League match against Sunderland.
"The injury is similar to the one suffered by the forward against Sunderland in September last year, however it is not considered to be as severe," Spurs said on their website.
"Harry will continue to be assessed by our medical staff while he undergoes his rehabilitation at our training centre."
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Kane has scored two league hat-tricks since the turn of the year to keep second-placed Tottenham at the front of the pack chasing runaway leaders Chelsea, who are 10 points clear.
(Reporting by Martyn Herman; Editing by Ken Ferris)
