Billups suffered the injury early in the second quarter and didn't return to the game after playing just seven minutes and scoring two points.
Clippers coach Vinny Del Negro said Billups would be listed as day to day but hoped he could return Saturday against the Brooklyn Nets.
"He's a little better," Del Negro said. "Hopefully, he'll be back by Saturday. We'll see."
Billups has played only 19 games this season while battling through a variety of injuries, but he said his groin strain wasn't serious and he felt he could be back on the court in time for Saturday's game.
"I'm not frustrated about this one," Billups said. "This is going to be a minor thing. It's really just day to day. It's just a groin tweak, and I'll be back soon."
The Clippers also will be without Eric Bledsoe, who has missed the past four games with a sore left calf, and Ronny Turiaf, who has missed the past two games with a sore right knee. Del Negro said both players also could be ready to return to the court Saturday.
Bledsoe's absence has been one of the reasons the Clippers' bench has struggled and the Clippers have lost three of their past five games.
"You need everybody," Del Negro said. "We're a different team when guys are in and out of the lineup. Like Bledsoe's skill and speed and the way he changes the game at times defensively and gets us out in the open court. We miss some of those things. With Chauncey and Bledsoe out, it changes the complexion of our team, there's no question about it."