Tavares may need surgery; he is expected to be ready by training camp in September.
Tavares, playing for Canada, took a hard hit from Latvia defenseman Arturs Kulda in the second period and struggled to get back to the bench before leaving for the dressing room.
The center had no points in four games in Sochi but a plus-3 rating and six shots on goal averaging 10:39 of ice time.
He is third in the NHL with 66 points in 59 games this season.
Canada coach Mike Babcock said after the game Wednesday that Tavares would be out for the remainder of the Olympics.
"As a friend that's tough to hear. As a teammate that's tough to hear. Quite frankly, as a fellow Canadian, it's really hard to hear," Islanders defenseman Travis Hamonic told his team's website Wednesday after the initial news Tavares would be sidelined.
"He's an important player for that team. You want your best players playing in each scenario. It's unfortunate that John got hurt and things worked out that way. There's a lot of depth on that team and they're going to push forward. On a personal standpoint and a friend point of view, it's tough to see a guy go through that."
Canada, which defeated Latvia 2-1, will play the United States in a semifinal game Friday (noon, NBCSN, CBC). The winner advances to the gold-medal game Sunday.