The club said the English forward "is expected to return to training in early March."
Along with missing the second leg of Tottenham's League Cup semifinal against Chelsea next week, Kane will be absent for a Champions League round-of-16 first-leg encounter with Borussia Dortmund on Feb. 13. The second leg is scheduled for March 5.
He's also likely to miss important Premier League matches against Leicester City (Feb. 10) and Chelsea (Feb. 27), and possibly the final north London derby of the season against Arsenal on March 2.
The 25-year-old Kane has endured ankle problems in the past, with an issue in 2016 forcing him to miss several weeks.
The two-time Premier League Golden Boot Winner winner currently sits in a three-way tie for the league's scoring lead with 14 goals in 22 matches and has found the back of the net 20 times in all competitions this season. Kane scored 30 league goals last term, but he finished second to Mohamed Salah's record-breaking 32 for Liverpool.
Overall, since manager Mauricio Pochettino arrived at Tottenham, Kane's scored a Premier League-high 119 goals, accounting for 36 percent of the club's total scoring output, according to Opta.
Additionally, Tottenham's also without forward Heung Min-Son - who's on international duty with South Korea at the Asian Cup - which will make things even more difficult without Kane:
Tottenham currently sit third in the Premier League table and nine points back of leaders Liverpool as they look to claim their first top-flight title since 1960.