The veteran center will be out at least three weeks, coach Sheldon Keefe said Tuesday. The season opener is Oct. 12 at Montreal.
Tavares, who turned 32 on Sept. 20, is entering his fifth season with Toronto and his 14th in the NHL.
He scored 76 points (27 goals, 49 assists) in 79 games last season and has 895 points (391 goals, 504 assists) in 949 career games with the New York Islanders (2009 to 2018) and Maple Leafs.
The Islanders drafted Tavares with the No. 1 overall pick in 2009.