The team said a bone spur was removed from the elbow and that he was expected to be fully recovered when spring training begins in 2013.
Sabathia has spent the last four seasons of his 12-year career with the Yankees and went 15-6 in 2012 with an earned run average of 3.38.
He went on the disabled list in August after developing soreness in the elbow, but returned to action on Aug. 24 and made seven more starts in the regular season and three in the playoffs.
In other baseball medical news Thursday, the Washington Nationals said arthroscopic surgery had been performed on the right shoulder of third baseman Ryan Zimmerman.
Zimmerman played in 145 games this season with a .282 batting average. He had 25 home runs and 95 RBI while helping Washington win the National League East title with the best record in the majors.