The team is listing Crawford as day to day, but he is expected to miss as many as 2-3 games while recovering from the injury.
Los Angeles' next game is Saturday against the New Orleans Pelicans.
Crawford was injured Wednesday against the Houston Rockets and did not play in the second half. He had eight points in 16 minutes before being taken out with 13 seconds left in the second quarter.
Clippers coach Doc Rivers was initially worried about Crawford's injury after the game.
"Personally, I'm a little concerned because no one was around him," Rivers said. "When guys get injured when nobody's around them, that always scares me. We'll know more tomorrow. He said he felt better. I think he'll be OK, but I've been around the league a while, so that's my concern."
Despite being a candidate for the Sixth Man of the Year Award, Crawford has started 23 games this season in place of J.J. Redick, who is sidelined indefinitely with a bulging disk in his lower back.
Crawford is averaging 19 points, 3.2 assists and 2.3 rebounds this season, his best season since he was with the New York Knicks in 2008-09. In his past 19 games heading into Wednesday, Crawford was averaging 24.2 points, nearly a 7.5-point increase over his scoring average through the first 40 games of the season.