Pena was injured in Saturday's 11-inning, 10-7 victory at Minnesota while swinging a bat. He continued to play the last two innings despite the injury.
"As tough as he was to go back up there and have another at-bat and turn that last double play, I've got to believe that if he heals up the way that we hope that it will, hopefully it won't run into a two-month ordeal," Kansas City manager Trey Hillman said.
"Hopefully it'll be four to six [weeks], and we'll get him back."
Pena was being used primarily for defensive purposes. At the plate, he was 0-for-11 in 10 games. His spot on the roster was taken by infielder Luis Hernandez, who was called up from Triple-A Omaha.
Dick Kaegel is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.