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.
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.
Introducing the new official NHL App, available for iPhone, iPad and Android smartphones and tablets. A host of new features and improved functionality are available across all platforms, including a redesigned league-wide scoreboard, expanded news coverage, searchable video highlights, individual team experiences* and more. The new NHL App on your tablet also introduces new offerings such as 60fps video, Multitasking** and Picture-in-Picture.
*Available only for smartphones
** Available only for suported iPads