Billups has missed four games with the injury. The Knicks are 3-1 without the 34-year-old veteran.
Billups suffered the injury last Tuesday against Orlando when he collided with Magic center Dwight Howard.
The Knicks hoped to have Billups back for Monday's game but he was ruled out prior to tip-off due to the lingering soreness in his thigh.
"He's still feeling some pain and until it goes away he won't play," Knicks coach Mike D'Antoni said before the game.
Backup Toney Douglas filled in for Billups and the Knicks didn't miss a beat against the Jazz, outscoring them 40-24 in a first quarter in which Douglas had 12 points and two assists. He finished with 20 points on 6-of-9 shooting and hit five of seven from beyond the arc.
"Hopefully we can get Chauncey back as soon as we can because we need to work with that, but this has been good for Toney," D'Antoni said.
Big man Ronny Turiaf missed Monday's game -- his third straight -- with a sore left knee and was replaced by Jared Jeffries. Jeffries finished with six rebounds, three assists and several hustle plays on loose balls in 23 minutes.
D'Antoni said before the game that Jeffries would remain the team starter after Turiaf's return.
Bill Walker will also missed his second straight game with a sore left knee. Walker predicted that he would be back for Wednesday's game in Memphis.
Billups has been a linchpin for the Knicks (31-29), averaging 23.3 points and six assists in four games with New York. Billups was acquired in the three-team, 13-player deal that brought Carmelo Anthony to New York on Feb. 22.
The Knicks are in sixth place in the Eastern Conference, just a game ahead of the Philadelphia 76ers. They trail the Hawks by 3½ games. They are 5-3 since acquiring Anthony and Billups.
Ian Begley is a regular contributor to ESPNNewYork.com.