Soria left Sunday's game after retiring only one of five batters he faced and said after the outing that his elbow felt "really bad."
Royals spokesman Mike Swanson said Monday the team believes Soria has some damage in the area of his ulnar collateral ligament.
Soria had Tommy John surgery on his elbow in 2003. He has been one of the best relievers in the American League since his rookie season of 2007, but his performance fell off last year. His ERA jumped to 4.03 and he had 28 saves, but lost the closer's job at times.