Polak, acquired last off-season from the St. Louis Blues, was a key shutdown player for the Leafs and had five goals and four assists in 56 games.
Toronto called up Petter Granberg from the AHL's Toronto Marlies on an emergency basis to play against the New York Islanders on Monday night. Granberg played 14:18 in the 4-3 overtime loss.
The Leafs' decision to have Polak undergo the operation came a day after interim coach Peter Horachek announced the same was being done with Stephane Robidas.
Robidas, 38, will have surgery to repair a torn labrum, rotator cuff and other damage in his left shoulder.
"Those are two pretty important guys, penalty-killing guys, defensive guys," Horachek said. "Guys that are leaders back there and character people back there."
Without Polak, Robidas and two defencemen who were traded — Cody Franson and Korbinian Holzer — Toronto's blue-line is down to Dion Phaneuf, Morgan Rielly, Jake Gardiner, Granberg and newcomers Eric Brewer and Tim Erixon.
Horachek said the injuries might lead to other Marlies call-ups. Andrew MacWilliam is the most likely option before the Leafs go on a Western Canadian road trip later this week.
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