Jack suffered the injury late in the third quarter of Saturday's victory over the Boston Celtics. It was initially diagnosed as a right knee sprain.
Jack said on Instagram after the game that the injury was the "worst pain I've ever felt in my life."
Jack, 32, finishes the 2015-16 campaign with averages of 12.8 points, 7.4 assists and 4.3 rebounds in 32 games.
He is set to make $6.3 million this season and next season, though only $500,000 of his 2016-17 salary is guaranteed.