Gionta will have surgery on Friday to repair the damage. He underwent the same procedure on his right biceps last year.
The 34-year-old Gionta played in only two of four games against the Ottawa Senators in the first round of the Stanley Cup playoffs and contributed one assist. The Canadiens trail 3-1 in the best-of-seven series after a 3-2 loss on Tuesday night.
The Pittsburgh Penguins will turn to Tomas Vokoun as their starting goaltender in place of struggling Marc-Andre Fleury for Game 5 on Thursday night against the New York Islanders.
Fleury gave up six goals in the Penguins' loss to the Islanders on Tuesday night. That performance came after he allowed five and four goals in Games 2 and 3.
The 36-year-old Vokoun has not played in the postseeason since the 2007 season with the Nashville Predators. But this year against the Islanders during the regular season, he was 3-0-0 with a 0.90 goals-against average and a .970 saves precentage.
Pittsburgh, the top seed in the Eastern Conference, and the Islanders are tied 2-2 in the first-round series.
Goaltenders Sergei Bobrovsky of the Columbus Blue Jackets, Henrik Lundqvist of the New York Rangers and Antti Niemi of the San Jose Sharks were named finalists for the Vezina Trophy on Wednesday.
The award is given annually to the top goalie in the NHL. Voting is done by general managers from the 30 NHL teams. The winner will be announced during the Stanley Cup Finals.
For the first time, all three finailists are European natives.