The team said Robinson would be evaluated on his progress toward returning in three weeks.
Robinson left Wednesday's loss in the first half with what the team called a right thumb sprain, and Knicks coach Tom Thibodeau had said he would be evaluated further Thursday.
Robinson, 24, is averaging 7.2 points and 8.9 rebounds per game, including 4.3 offensive boards a night, the second most of any player in the league behind Grizzlies center Steven Adams.
His absence will be a significant blow to New York (25-21), which sits tied with Miami for sixth place in the Eastern Conference standings. The Knicks are outscoring teams by 8.2 points per 100 possessions when Robinson is on the court -- easily the best mark of any rotation player -- and are being outscored by 1.1 points when he's on the bench.
With Robinson sidelined, New York will turn to the combination of Isaiah Hartenstein and Jericho Sims at the pivot, and could also potentially utilize some smaller lineups with either Julius Randle at center or with Randle and third-year forward Obi Toppin playing together in certain matchups.