Francis had the operation Wednesday at the Steadman Hawkins Clinic in suburban Greenwood Village, Colo. He is expected to miss the entire season.
The Rockies say he'll begin rehabilitation immediately, but no date has been set for him to resume baseball activities.
Francis struggled with inflammation in his shoulder last season, when he went 4-10 with a 5.01 ERA. He came to spring training hoping to pitch through pain but decided last week to have surgery.
In five years with the Rockies, Francis is 51-44 with a 4.74 ERA.