Kane was diagnosed with ligament damage in his right ankle after injuring it last Sunday against Millwall in the FA Cup, the club announced on Tuesday.
When Kane suffered his previous injury in September, the forward was forced to spend seven weeks on the sidelines before returning for a 1-1 draw against Arsenal.
Kane faces an extended spell of recuperation but Tottenham emphasised that the injury appeared less serious than the ankle problem that kept him out for seven weeks earlier this season.
"Harry will continue to be assessed by our medical staff while he undergoes his rehabilitation".
The 23-year-old missed five Premier League games and two EFL Cup matches after twisting his ankle tackling Sunderland's Papy Djilobodji.
Tottenham Hotspur have released an update on injured striker Harry Kane.
The Argentine will be hopeful that Kane can make it back for that crucial match against Chelsea and for the rest of their Premier League run-in where they are aiming to finish in the top four.
Kane will likely not play for England during the global break, meaning Gareth Southgate will be without his form striker for the friendly against Germany next Wednesday and the World Cup qualifier with Lithuania.
The clash against United is set to be Tottenham's final fixture at White Hart Lane. He netted on his first game back, at rivals Arsenal.