The 30-year-old suffered the injury during the first half of Spurs' 1-0 win over West Brom.
It forced him to withdraw from the England squad for Wednesday's friendly with Brazil at Wembley.
He will now also miss Tottenham's Premier League match against Newcastle on Saturday and the Europa League last-32 home and away ties against Lyon. He could also be absent for the league match at West Ham.
Tottenham will certainly hope Defoe is available for the north London derby at home to Arsenal on Sunday, March 3.
The 30-year-old's injury leaves Spurs short of experienced options in attack, although boss Andre Villas-Boas is hoping to have Emmanuel Adebayor back from African Cup of Nations duty for Saturday's match at White Hart Lane.
The striker is expected to report back for training on Friday after his Togo side were knocked out of the tournament at the quarter-final stage by Burkina Faso.
Clint Dempsey could also be deployed in attack for Spurs, with youngsters Jon Obika and Harry Kane two other options.
Tottenham were linked with a move for Nacional striker Leandro Damaio but opted against signing a striker in the January transfer window with Villas-Boas explaining it was "a risk we were willing to take".
Defoe is the club's leading scorer this season with 14 goals in 32 appearances.