Bergman was struck on his left hand by a line drive last Friday against the Milwaukee Brewers. The fracture was confirmed by the team's medical staff after the swelling in his hand subsided.
While the Rockies had not yet formalized the move, manager Walt Weiss said the team planned to call up Yohan Flande from their Triple-A affiliate in Colorado Springs to start Wednesday's game against St. Louis.
Flande, making his major league debut, will be the 12th pitcher to start a game for the Rockies this season, most in the big leagues.
He will be opposed by Marco Gonzales, who also will be making his major league debut. Gonzales was the Cardinals' first-round draft pick last year.