The surgery was performed in Birmingham, Ala., by Dr. James Andrews.
The 26-year-old Burke hit .276 with a career-high nine home runs and 40 RBI this season. He had 23 doubles, 11 stolen bases and 58 runs scored.
Burke played five positions, including 69 at second base and 38 in center field.
Burke hurt his shoulder crashing into the wall at Denver's Coors Field in May and then re-injured it in June while batting against the Chicago Cubs.