The Braves said Wednesday the procedure was performed on Tuesday by Dr. James Andrews in Gulf Springs, Florida.
General manager John Coppolella told The Associated Press Rodriguez will miss an "indeterminate period of time." Coppolella said the team "won't rule him out for the year." Rodriguez throws and hits right-handed.
Rodriguez, who agreed to an $11.5 million, two-year contract with Atlanta in November, hurt his shoulder when a vehicle he was driving was rammed by a stolen police car in Miami on Jan. 28. The driver of the stolen car was killed. Rodriquez's wife Giselle and two of their children were hospitalized with injuries she said on her Twitter account were not life-threatening.
The Braves acquired second baseman Brandon Phillips from Cincinnati on Sunday.