Bargnani, the team's second-leading scorer, suffered the injury Wednesday in a game against Philadelphia. The Knicks lost that game, their fifth straight setback.
New York obtained Bargnani prior to this season in a trade with Toronto. He has averaged 1.3 points and 5.3 rebounds per contest.
The Knicks have a 15-27 record this year, one season after they won 54 games and reached the Eastern Conference semifinals.