When Kane hobbled away from Bournemouth's Vitality Stadium on Sunday having been substituted early in the Premier League win there were fears he had sustained serious damage.
However, the first update on his condition from Spurs since the weekend offered a more optimistic scenario.
"Preliminary assessments have confirmed that (Kane) has damaged lateral ligaments in his right ankle," the north London club said on their website (http://www.tottenhamhotspur.com).
"The England striker sustained the injury following a challenge in our 4-1 win over Bournemouth on Sunday and is expected to return to first team training next month."
Kane has scored 39 goals for club and country this season and is expected to be England's main striker at the World Cup finals in Russia which start in June.
He will miss Tottenham's FA Cup quarter-final at Swansea City this weekend and England's friendly internationals against the Netherlands on March 23 and Italy on March 27.
"Disappointing to be out until next month but injuries are part of the game," Kane said on Twitter later on Wednesday.
"Will do everything I can to get back out there asap."
England manager Gareth Southgate will select his squad for the two friendlies on Thursday.
Kane, who is almost certain to miss Tottenham's key Premier League game at top-four challengers Chelsea on April 1, had two spells on the sidelines last season with right ankle problems.
(Reporting by Martyn Herman; editing by Ken Ferris and Christian Radnedge)
