Spurs confirmed on Thursday (NZDT) that damage to the ligaments in Kane's right ankle has ruled him out of action until April.
The striker, joint top-scorer in this season's Premier League with 24 goals, sustained the injury in a clash with goalkeeper Asmir Begovic during Spurs' 4-1 win at Bournemouth on Monday.
Kane will miss Sunday's FA Cup quarter-final against Swansea City, as well as England's friendlies against Netherlands and Italy.
"Disappointing to be out until next month but injuries are part of the game," Kane said on Twitter.
"Will do everything I can to get back out there asap."
Kane - expected to be out of the Premier League game at Chelsea on 2 April - will join Tottenham team-mate Toby Alderweireld in the treatment room and the defender was quick to show his support to the striker after the setback.
"Get well soon mate!" said Alderweireld in response to Kane's tweet.