The team recalled righty Mitchell Boggs from Double-A Tulsa on Saturday to take Betancourt's place in the bullpen.
Betancourt's son, Rafael, told the Rockies his father was ill Thursday night after a team workout at Coors Field.
"His son actually came in and said, `Hey, check with my dad, he was real sick last night.' That's how we found out," head athletic trainer Keith Dugger said.
Assistant trainer Scott Gehret examined Betancourt on Friday afternoon and determined he was suffering from appendicitis.
"Scotty evaluated him and said, `Duggie, take a look, it looks like his appendix.' I looked at him and agreed with his diagnosis," Dugger said. "I sent him to Dr. (Allen) Schreiber. He said it was probably appendicitis and sent him to the hospital."
Betancourt's appendix was removed not long before it would have burst, Dugger said.
"I don't think they had a whole lot of time left before that thing ruptured," Rockies manager Walt Weiss said. "Everything went well, but he's going to be down for a little bit."
Betancourt is expected to miss up to three weeks. He 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.
The Rockies will adjust their bullpen to compensate for the loss of Betancourt. Rex Brothers, a left-hander, will serve as the closer. Brothers had four saves in five chances when he took over the role when Betancourt was on the disabled list because of a groin strain for four weeks in June.
Brothers didn't allow a run in 30 innings over 32 appearances from April 10-June 28. He is 2-0 with a 1.11 ERA.
Betancourt's illness is another blow to the Rockies, who were rounding back to health. Shortstop Troy Tulowitzki returned last week from a broken rib, and outfielder Dexter Fowler was also activated before the All-Star break after missing 15 days with a sore right hand.
"It looked like we were getting healthy again and this pops up," Weiss said. "Every team has to deal with it at some level. We'll make due while Raffy is out."