The team announced Wednesday that surgery will be performed next week.
The injury occurred Monday night in a preseason game against the Seattle Kraken when Pelletier, 22, was pushed into the boards by Marian Studenic. As Pelletier writhed in pain on the ice, his teammates went after Studenic.
Studenic received a boarding major and game misconduct following the hit.
The Flames selected Pelletier, a Quebec native, with the 26th overall pick of the 2019 NHL draft. The 5-foot-9 winger appeared in 24 games and posted seven points (three goals, four assists) in an average of 14:11 minutes on ice per game.
Before the preseason game, Pelletier talked about his excitement for the upcoming season.
"My main goal is to start the year in the NHL," he said, according to Sportsnet. "But for me I think it's just to, every day, be the best player and be the guy that works the hardest.
"It's bringing positivity, playing with pace, trying to create offensive chances, and just to show, whether I'm on the first or fourth line, be a role guy and show that I belong in the NHL and to leave no doubt for the coaches."
The Flames open the regular season at home Oct. 11 against the Winnipeg Jets.