Crawford was injured after turning his ankle chasing a double from Reds outfielder Chris Heisey.
"It doesn't look good," Dodgers manager Don Mattingly said, via MLB.com. "The video didn't look good."
Crawford was replaced in left field by Scott Van Slyke and went to the clubhouse to take X-rays, which were negative.
"My leg just slipped and it swelled up real quick. They're going to put me on the DL. I think it's going to take a while," Crawford said. "It's very frustrating, I'm in pain, I'm in this boot, and they said it's supposed to feel worse tomorrow."
Crawford is batting .267 with four home runs and 18 RBI this season. CHEN: Dodgers prospect Joc Pederson could be the next big thing