Sanchez initially injured the thumb while working in the weight room on Thursday and underwent the surgery Saturday in Vail, Colo. The team described the injury as a torn ligament in the thumb of his non-throwing hand.
The Broncos acquired Sanchez for a conditional seventh-round pick in a trade with the Philadelphia Eagles in March.
Sanchez, a Southern California product, played his first four seasons for the Jets before becoming a backup the last two for the Eagles. He is 37-35 as a starter and is currently the front-runner to replace Peyton Manning, who retired after winning the Super Bowl.
Information from The Associated Press was used in this report.