Spurs tweeted this afternoon that he has damaged his lateral ligaments in his right ankle.
He injured the same ankle again in Tottenham's FA Cup quarter-final victory over Millwall in March 2017.
England's 2018 FIFA World Cup preparations will also be affected by Kane's injury, with the player also poised to miss back-to-back friendlies against the Netherlands and Italy on Friday, March 23 and Tuesday, March 27.
England will face Tunisia, Belgium and Panama in the World Cup group stage in Russian Federation.
They visit Swansea City this weekend in the hopes of progressing through to the FA Cup semi-finals, a match Kane will miss, and then face Chelsea early next month to contest for a Champions League position.
And while Kane has suffered two similar injuries to the same joint, this latest setback is not as bad as his previous knocks and should ensure that he has plenty of preparation for the major tournament in Russian Federation next June.
Despite concerns over how long Kane may be ruled out for, with the World Cup just three months away, his previous ankle problems were of differing severity and time-frames for recovery.
With 24 league goals, Kane is level with Liverpool s Mohamed Salah in his quest for a third straight Premier League golden boot.
Kane, who has scored 35 times for Tottenham this season, would only have a handful of matches remaining this term to prove his fitness to England manager Gareth Southgate.
"We are here to develop, to help the club achieve and win titles", said the Argentine.