Crawford participated in drills other than throwing and hitting Thursday, saying the stiffness cropped up two days ago.
"It flared up on me," said Crawford. "We're just being careful. I don't think it's [anything] crazy, just everybody is being very careful. From what I'm hearing, this stuff happens and I wouldn't be surprised if it happens again.
"We just have to stay on top of it. I don't look at it as a major setback. If I had to, I could do the things I'd have to do."
Manager Don Mattingly said Crawford might have thrown too much in his rehab from Tommy John elbow surgery.
"It's not uncommon going through this," Mattingly said. "We want to be cautious with Carl. There's plenty of time before Opening Day. I don't know if it's a setback, but it's a pause. We've had him doing so much, and this guy is a working machine. He wants to get out there, but Sue [Falsone, trainer] wants to be cautious. We don't want to push it."
Kemp said he's passed the big tests in his mind after surgery to repair a torn left shoulder labrum.
"I can swing and miss and I can check-swing, and I don't feel anything," he said. "Last year, I would feel it get tingly down my arm. But that's gone. I think it's time to play a game."
Mattingly originally was planning to ease both Crawford and Kemp back into game action as designated hitters. But he said Kemp will likely play the field as well because his injury, unlike Crawford's, doesn't involve his throwing arm.
"I don't necessarily have to DH Matt," said Mattingly. "When we feel like he's ready to go, he can play the field. It's not like Carl."
Ken Gurnick is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.