The England international suffered the blow during the team's 4-1 victory over Bournemouth at the Vitality Stadium on Sunday.
Kane, who has scored 35 goals in all competitions this season, was forced off the pitch in the first half after colliding with goalkeeper Asmir Begovic.
On Twitter, Spurs confirmed that the 24-year-old has suffered ligament damage in his right ankle and is expected to be on the treatment table for the rest of the month before returning to training in April.
The post read: "Preliminary assessments have confirmed that @HKane has damaged lateral ligaments in his right ankle.
"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."
The update means that Kane will miss England's upcoming internationals, but has a chance of making the World Cup.