Moore left his start on Tuesday night in Kansas City because of discomfort in the elbow and the second or two MRI exams disclosed the partial tear, which gave him hope that he might be able pitch again this season.
The left-hander hopes that rest and treatment will calm things down in the joint and he plans to play catch later this week before deciding whether or not to have the surgery, which could sideline for a year or more.
The 24-year-old Moore was 17-4 with a 3.29 earned-run average, a 1.30 WHIP and 143 strikeouts in 150 1/3 innings last season. He is 0-2 this season with a 2.70 ERA.
The Rays are not sure who will replace him in the rotation.