The surgery will be performed Friday by Dr. Gregory Pearl at Baylor University Medical Center in Dallas. The recovery time is 10 to 12 weeks.
Cobb is expected to assume his normal winter throwing routine and be completely recovered by the start of spring training.
The rookie was placed on the 15-day disabled list last Sunday, one day after Cobb felt what he described as a dead feeling in his hand during a start against the Oakland Athletics.
Cobb went 3-2 with a 3.42 ERA in nine starts this season.