But it also means that Kane should be back for the end of the season and will nearly certainly be okay for the World Cup.
In a brief statement posted to the club's official website on Wednesday afternoon, Tottenham said: "Preliminary assessments have confirmed that Harry Kane has damaged lateral ligaments in his right ankle".
"Disappointing to be out until next month but injuries are part of the game", Kane tweeted.
England's first World Cup match is on 18 June against Tunisia. "Will do everything I can to get back out there [ASAP]".
Kenya Sevens team hint mistreatment from rival nations on the sevens circuit
Sevens Series leaders South Africa claimed the bronze medal after beating the USA 29-7 with five tries to their opponent's one. France and Spain both progress to the Challenge Trophy quarter-finals, their end of day clash resulting in a 12-12 finish.
(Files) Tottenham Hotspur's English striker Harry Kane lies on the floor after being fouled during the football match against Watford at Vicarage Road Stadium in Watford, on December 2, 2017.
With the World Cup just three months away, Three Lions boss Gareth Southgate will also be eager to find out how long Kane could be sidelined for.
The England forward suffered the problem during Sunday's 4-1 Premier League win at Bournemouth.
Kane would miss Spurs' FA Cup quarter final at Swansea on Saturday, March 17, and also a semi final if they progress and four league fixtures after the global break.
However, Pochettino insists Kane can fulfil his ambitions by staying at his boyhood club.