Waldrop felt discomfort in a throwing session on Thursday, and he will be shut down for at least a few days.
"I think he's OK," Ryan said. "We just don't have enough time."
Waldrop said he first felt the discomfort before his outing against the Yankees in Tampa on March 23, and that it only worsened from there.
It's a tough break for Waldrop, as the sinkerballer had a strong chance to make the club after posting a 1.50 ERA in six Grapefruit League appearances.
"It's disappointing but it's baseball," Waldrop said. "Injuries happen. I just have to take care of it right now and move forward. It's a long season. It's not like this is something that's going to require surgery, so I'm just going to kind of deal with it and get better, get healthy."
Waldrop, 26, added that he hopes to get back on the mound soon, and that he's still proud of the way he performed this spring.
"It's a little setback, but I'm not going to keep my head down," Waldrop said. "This is something that I'll come back from and get healthy, and I'll be all right."