The team recalled righty Mitchell Boggs from Double-A Tulsa on Saturday to take Betancourt's place in the bullpen.
Betancourt was feeling ill Friday afternoon and was sent to a medical center. He was then moved to a hospital where he underwent an emergency appendectomy.
He is expected to miss up to three weeks.
Betancourt is 2-3 with a 3.16 ERA and 15 saves in 16 chances in 28 games this season.
Boggs was acquired on July 9 from the St. Louis Cardinals, with whom he was 0-3 with an 11.50 ERA in 15 games. After joining the Rockies organization, Boggs was sent to Tulsa. He posted one save in four appearances.