The 22-year-old returned to London earlier this week after suffering the injury on international duty with Brazil on Monday and now looks likely to miss the first two months of the new Barclays Premier League season.
A statement on www.tottenhamhotspur.com read: "Following consultation with an independent knee specialist, Sandro underwent surgery on his left knee in London."
It continued: "Sandro withdrew from Brazil's Copa America campaign on Tuesday due to injury with scans confirming he had torn his lateral meniscus, as well as suffering a calf strain.
"The specialist has advised a three-month rehabilitation period before a return to full training."
Sandro was sent for a scan after complaining of pains in both his calves and his knee in training during Brazil's Copa America campaign in Argentina.
Results showed that the midfielder had ruptured the meniscus in his knee - an injury which requires surgery and usually takes around a month to heal - but specialists have now delivered a worse prognosis for Spurs.
Sandro has become a popular figure at White Hart Lane since his move to the club in March 2010.
The Brazilian, who signed from Internacional for £8million, played 26 times for Harry Redknapp's team last season, and made his international debut in 2009.
The injury could further strengthen Spurs' already fierce resolve to hang on to Luka Modric, who is believed to have been the subject of two bids from Chelsea.
Source: PA
Source: PA