Rays general manager Andrew Friedman said Moore would see Dr. Andrews in the next two days for "a more thorough exam."
Moore left in the fifth inning Monday night with discomfort in his elbow after throwing a changeup to Kansas City Royals right fielder Nori Aoki.
Friedman says it is "standard practice" for the team to put a pitcher on the DL go to these situations.
Moore won 17 games last season, but also missed 31 games with a sore elbow.
The Rays recalled left-hander Jeff Beliveau from Triple-A Durham.
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