The 25-year-old sustained the injury on Monday against Slovakia.
"It’s disappointing to see a player like Brandon get hurt at his first world championship," said Ron Francis, a member of Canada’s management group, in a press release. "He is a key player who brought so much to the team, and although he won’t be able to continue, we were impressed with his work ethic on and off the ice. We wish him all the best in his recovery."
Montour was representing Canada for the first time at any tournament, going without a point in three preliminary-round games. He will return to Buffalo for further evaluation.
The Sabres acquired Montour from the Anaheim Ducks in exchange for defenceman Brendan Guhle and a 2019 first-round draft pick at this year’s NHL trade deadline.
Canada will be back in action on Thursday morning when they face France in the preliminary round.