The team says an MRI on Tuesday confirmed Billups' injury.
Billups will return to Los Angeles on Thursday for further evaluation. The Clippers say a date for surgery hasn't been determined.
The five-time all-star, whom the Clippers claimed off waivers in December, was averaging 14.9 points and 4.0 assists in 30.4 minutes per game this season.
Billups was having a huge night Monday, scoring 11 of his 18 points in the fourth quarter when he turned to run up the court and buckled to the ground with 5:48 left in the game. He was surrounded by trainers and teammates, but needed assistance on both sides to make it off the court.