Tavares, 23, was hurt during Canada's Olympic semifinal Wednesday against Latvia. Canadian team officials immediately ruled him out for the rest of the Olympics.
The Islanders said Thursday subsequent examinations determined Tavares tore the medial collateral ligament and had a meniscus tear in his left knee.
The NHL team website had a posting confirming the injury and said Tavares would miss the remainder of the season.
Tavares, the first overall selection in the 2009 NHL draft and the Islander's captain, is third in scoring this season in the NHL with 66 points in 59 games. He has 136 goals and 179 assists over 350 NHL games in his career.
The Islanders are last in the NHL Metropolitan Division with 52 points.