Ranked No. 8 on the Orioles' prospect list by MLB.com, Kline, 21, is 1-2 this season with a 5.86 ERA in seven starts for Class A Delmarva.
The Orioles expect Kline to recover and pitch again this season. He sustained the injury during a between-starts workout.
AJ Cassavell is a reporter for MLB.com. Follow him on Twitter @ajcassavell. This story was not subject to the approval of Major League Baseball or its clubs.