Pena broke his left hamate bone when he fouled a pitch off in the 10th inning against Minnesota on Saturday. He finished that at-bat, hit a flyball for the final out of the 11th with his left hand off the bat, then took a flip from second baseman Alberto Callaspo for a game-ending double play in the bottom half.
Pena, who was placed on the DL on Sunday, will have surgery to remove the hook part of the hamate.
Manager Trey Hillman announced the diagnosis before Kansas City's game against the Chicago White Sox on Monday night. He says Pena could be out from four weeks to two months, depending how it heals.