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The French international suffered medial collateral ligament damage during a 1-0 defeat at Southampton on New Year's Day.
"Following a clinical assessment and scans, Moussa Sissoko has today undergone surgery to the medial collateral ligament in his right knee," Tottenham said in a statement.
"Our medical staff will monitor Moussa's recovery before he commences rehabilitation with a view to returning to training in early April."
Sissoko will miss at least 10 Premier League matches, including clashes with Liverpool, Manchester City, Chelsea and Manchester United, as well as both legs of Tottenham's Champions League last 16 clash with Bundesliga leaders RB Leipzig.
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Jose Mourinho will also be without talisman Harry Kane in the coming weeks after the England captain suffered a hamstring tear at Southampton.
Club captain Hugo Lloris and Ben Davies are long-term injury absentees, while Mourinho claimed Tottenham's record signing Tanguy Ndombele is "always injured" after the French midfielder limped off in the first half at Southampton.
kca/jc