The All-Star is out with a sore left elbow. He had hoped to return this weekend, but struggled Wednesday during a 55-pitch bullpen session.
Moore said he won't throw again until Sunday.
The Rays said they don't consider this to be a setback. They said the team is taking a cautious approach.
"I felt good, but good isn't great, and great is 100 percent," Moore said. "What we're really aiming for is to be back out there and be 100 percent."
Moore is 14-3 with a 3.41 ERA.
Also, Rays manager Joe Maddon confirmed that Alex Cobb will pitch in the majors Thursday night for the first time since being hit in the head by a line drive on June 15.