Moore left in the fifth inning of Monday's 4-2 loss after feeling discomfort in his elbow while throwing a pitch to Nori Aoki. The Rays were awaiting MRI results.
Rays general manager Andrew Friedman said an MRI exam on Tuesday of Moore's elbow "is inconclusive" and the All-Star would see Dr. Andrews in the next two days for "a more thorough exam."
"It is our standard practice to have a pitcher go to the DL in these situations," Friedman said. "He'll be out 15 days; that's all we know right now. We don't know much beyond that. We'll know more in the next few days. The fact that he feels good is a positive sign."
Moore was 17-4 with a 3.29 ERA last year, when he was on the disabled list from July 31 to Sept. 3 because of a sore elbow.
"I would say it's quite a bit different in how it feels, in how it dangles, with regards to soreness," Moore said before Tuesday night's game. "The discomfort is similar. The severity has jumped from what I was feeling. It's frustrating."
Moore said he realizes surgery is an option.
"I would say it's a possibility," Moore said. "I think the procedure they'll be doing will give a better way to tell the severity. If they had one way to tell, up close, tomorrow will be the way to tell."
Friedman said: "Nothing is ruled out until he has a more thorough exam. "He'll have his elbow examined and they'll use a dye and look inside his elbow.. We are waiting with baited breath."
Moore said if surgery is needed, "the sooner the better."
"I know I'm not having surgery tomorrow," Moore said. "I'm not going to be stewing over it. It will depend upon the severity. If I can pitch with it, we'll see. It'll be a difficult process."
Manager Joe Maddon conceded Moore's condition was "worse than what we thought before."
"We'll have further tests with Dr. Andrews and it might end up being better than we thought," Maddon said. "We just don't know. We're going to gather info, be patient and make an informed, unemotional decision."
Tampa Bay recalled left-hander Jeff Beliveau from Triple-A Durham to fill the roster spot Tuesday. Beliveau has made 23 big league relief appearances, 22 in 2012 with the Chicago Cubs and one in the Rays' final game last season.