The 30-year-old suffered the problem during the first half of Spurs' 1-0 win over West Brom in the Premier League last Sunday.
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 on 25 February.
Defoe'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.
"He had issues to take care of as the tournament finished for Togo, so at the moment we're trying to see if we can have him back either for today or tomorrow's training session," said Villas-Boas.
"Obviously we have to take a look at him first. We don't have any news regarding injuries from him, so he's going to be selected for sure. I have to make a decision whether he will be in the starting XI or not."
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's Brazil international 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.
You can only watch the best Barclays Premier League coverage here on Sky Sports. Watch Spurs v Newcastle exclusively live on Sky Sports 2HD, 3D and Sky Go from 12:00pm on Saturday 9th February. Click here for more details