The A's said Friday they expect to make a decision on Crisp's playing status this weekend. He hasn't played since leaving a game Tuesday in Houston with a stiff neck. He suffered a similar injury the past season.
"If you talk about surgery, that probably means a bad outcome, as far as his playing career," manager Bob Melvin said Friday.
The 35-year-old Crisp had an MRI on the neck Wednesday, but Melvin said it did not reveal anything the A's didn't know last year.
"We're going to have to deal with it like we did last year," Melvin said. "If there are issues, we'll give him some time off. If there are significant issues, we'll DL him. Obviously, this is a dicey injury, and we're going to have to be careful with it."
Crisp, who had surgery on his elbow in early April, is batting .044 in 13 games this season.
Mujica fractured and cut his right thumb Thursday while fielding a ground ball hit by the Rays' Bobby Wilson. Because the stitches will remain in Mujica's hand for several days, the A's decided to put him on the disabled list. They are hoping the right-hander can resume throwing shortly after the swelling goes down.