Moore left Monday's start against the Kansas City Royals in the fifth with left elbow soreness after delivering a pitch.
Moore, 24, was then sent for an MRI to confirm the injury, and the team said the results were inconclusive. The Rays said the Moore will be sent to orthopedic surgeon Dr. James Andrews for further evaluation.
"Just talking to guys who have been hurt and what that feels like when it is your ligament, I had zero inflammation," Moore said after the game. "My brother tore his elbow in 2008 or 2009. He had a completely different feeling with his elbow injury."
In two starts this season, both losses, Moore has only allowed three earned runs in 10 innings, striking out six and walking five. SI.COM STAFF: Power Rankings: Detroit Tigers nab top spot in first week of voting