Defoe, 30, picked up the problem in last weekend's 1-0 win over West Brom.
He missed England's 2-1 friendly victory over Brazil on Wednesday night, and will now be unavailable for Premier League matches against Newcastle United and West Ham, plus both legs of the Europa League knockout tie with Lyon.
Boss Andre Villas-Boas, who has been without Emmanuel Adebyor because of the African Cup of Nations, acknowledged that it could have been worse.
"It’s good news in the end because it could have been further damage to his ankle," he said.
"We're trying to establish the best flight connections for (Adebayor)."
He added that Togo striker Adebayor could be back as soon as this weekend.
The injury to Defoe left Villas-Boas bemoaning his failure to sign a forward in the January transfer window, but the 'strikerless' formation of Clint Dempsey, Gareth Bale and Lewis Holtby saw Spurs beat the Baggies anyway.