"Nothing alarming as we speak," Canadiens general manager Marc Bergevin said Thursday before the surgery. "As you know, Carey played every minute of the playoffs and he performed very well. It's certain that, as in the case of the majority of players, there were injuries.
"He's seeing the doctor the end of this week. We're not expecting anything major. … Maybe just six or eight weeks, with a small chance that it might be longer, but we don't know as we speak."
A recovery of 12 weeks would take until Oct. 15. Montreal opens next season Oct. 13 at the Toronto Maple Leafs.
The Canadiens said Price also has a hip injury that will not require surgery.
Price helped Montreal reach the Stanley Cup Final, going 13-9 with a 2.28 goals-against average, .924 save percentage and one shutout in the Stanley Cup Playoffs. Montreal reached the Cup Final for the first time since 1993 and lost in five games to the Tampa Bay Lightning.
The 33-year-old was left unprotected by the Canadiens for the 2021 NHL Expansion Draft presented by Upper Deck on Wednesday, but the Seattle Kraken selected Montreal defenseman Cale Fleury.
Bergevin said he wasn't concerned Montreal would lose Price to Seattle.
"We had a plan B, for sure. Carey and me, we talked about it at length," Bergevin said. "But the risk was minimal for us."
Price is 360-257-79 with a 2.50 goals-against average, .917 save percentage and 49 shutouts in 707 regular-season games. In 2014-15, he was voted winner of the Vezina Trophy as the NHL's best goalie and was elected winner of the Hart Trophy voted the NHL most valuable player. He has five seasons remaining on the eight-year contract he signed with Montreal on July 2, 2017.
Bergevin also said center Jonathan Drouin is expected to be at training camp. Drouin took a leave of absence from the Canadiens in late April and hasn't played since. Bergevin and coach Dominique Ducharme met with Drouin early this week.
"Dom and I had a very good conversation [with Drouin]," Bergevin said. "'Jo' feels great. He's focused and he's ready to go, so I expect Jo to be in Montreal first day of camp.
"It's huge. I think when Dom took over (from fired Claude Julien on Feb. 26), we saw the best hockey Jo ever played in the Montreal uniform. After that, we all saw his game drop. Knowing now why that happened, and that it's been taken care of, we're pretty excited to see Jo back … that's a positive for us."
The 26-year-old has been with the Canadiens since 2017-18, after he was acquired in a trade with the Lightning. He scored 23 points (two goals, 21 assists) in 44 games last season before taking his leave, and has scored 232 points (69 goals, 163 assists) in 393 NHL regular-season games.
Montreal will not have defenseman Shea Weber next season. The Canadiens captain has multiple injuries and his playing career is in doubt.
The 35-year-old scored six points (one goal, five assists) and averaged 25:13 of ice time playing all 22 playoff games this postseason.
"It will be impossible to replace Shea Weber, what he brings to our team on and off the ice," Bergevin said. "We'll try our best, but I know deep down that you can never replace Shea Weber.
"Obviously, we need to somehow replace his minutes, defensemen that will get more responsibility as we move forward. We'll look closely to the market, either via trade or free agency to try to at least, to a degree, replace Shea, if we can."
NHL.com columnist Dave Stubbs contributed to this report
