The Brazil international was forced off after landing awkwardly in their 0-0 draw with Queens Park Rangers in the league on Saturday.
"Following consultation with the knee surgeon, the club can report that Sandro is expected to be sidelined for the rest of the season," Spurs said on their website.
The 23-year-old has made 27 appearances for Tottenham this season.
Spurs, who host Premier League leaders Manchester United on Sunday (1600 GMT), are fourth in the table with 40 points from 22 games.
Andre Villas-Boas will resist the temptation to enter the transfer market to sign a replacement, however.
"The only thing we have done at the moment is hold on to our midfielders, the ones who are here," Villas-Boas said.
"We have put on hold the movement of Jake Livermore's possible loan to another club. It is not out of the question, I think we are still pretty happy with what we have.
"We have to be careful. We still have a couple of weeks before the market closes, so we have to be careful with the decision and it will be something we hold on to and see how we go."
When asked if he was lining up any new arrivals the Portuguese replied: "It is not impossible but it is unlikely. At the moment there is nothing."
England international Scott Parker is the likely replacement for Sandro, with the former West Ham skipper only just returning from an Achilles problem.
The 32-year-old has not started a Premier League game since April but has returned in recent weeks.