Bergman was injured Thursday night in the Rockies' 13-7 loss to the St. Louis Cardinals. He is 1-3 with 5.89 in nine games, including one start.
Before Friday's game against the Pittsburgh Pirates, the Rockies also recalled right-handers Miguel Castro and Jordan Lyles from Triple-A Albuquerque and optioned right-hander Andrew Oberg to that club.
Castro made six relief appearances and posted a 1.50 ERA. Lyles began the season in Colorado's rotation and was 1-1 with a 7.64 ERA in four starts but will be used in long relief.
Oberg had a 4.76 ERA in eight relief outings.