He says he will have the operation Wednesday and be ready in time for training camp in September.
Bernier missed five games in March due to the injury.
He then aggravated the problem April 3 against the Boston Bruins and finished the season on the sidelines.
"I felt pretty good," he said. "It was sore but my range, my stretching was fine. I think a lot of players play through that."
Meanwhile, forward Joffrey Lupul says he's recovering after knee surgery and doesn't expect his off-season training to be impacted.
Forward Phil Kessel says he was "good enough" through the end of the season despite a bruised right foot while James van Riemsdyk wouldn't reveal any specifics on his injury.
Bernier was 26-19-7 with a 2.68 goals-against average and a .923 save percentage this season.
The Leafs missed the playoffs after posting a dismal 6-14-2 record down the stretch.
"We all know as a group that we didn't play to our potential all year," said Bernier. "We waited too long to turn the switch on and start playing some good hockey."
The injury likely means Canada will not be able to call on Bernier for next month's world hockey championship in Belarus.