The Brazilian was forced off midway through the first half of Spurs' 0-0 draw with QPR on Saturday, with Scott Parker coming on to replace him, and the midfielder's recovery schedule will be assessed over the next few days.
Following his operation, Sandro tweeted: "Sorry guys, but this one really got me, the beast is hurt.
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The midfielder's absence comes as a considerable blow to Tottenham manager Andre Villas-Boas, with Spurs currently sitting third in the Premier League table and still fighting in both the Europa League and FA Cup.
Sandro joined the north London side from Brazilian club Internacional in 2010 and has made 80 appearances for the club during his time in England, scoring two goals.