The team announced the surgery in a statement Tuesday. It didn't say which hand Humber hurt.
Humber has played primarily on special teams during his two seasons in Indianapolis. He assisted on one special-teams tackle last Sunday against the New York Giants.
The Colts also said wide receiver Anthony Gonzalez and safety Bob Sanders won't play against the Broncos. Gonzalez is recovering from a sprained right ankle, and he told The Indianapolis Star that doctors have told him he'll be out "four to six (weeks)." Sanders had surgery last weekend to repair a torn biceps muscle in his right arm.
The Colts said they have released former starting left tackle Tony Ugoh from injured reserve. He was put on the waived-injured list Sept. 8.
The Associated Press contributed to this report.