The surgery was performed by Dr. Neal ElAttrache on Wednesday in Los Angeles. Dr. ElAttrache, using Parker's revision UCL graft that was done two years ago, reconstructed the medial compartment of Parker's elbow, including reconstruction of the flexor tendon and ulnar collateral ligament complex.
Parker will return to Arizona on Saturday.
Parker had his second Tommy John surgery in March 2014 and hasn't pitched in the majors since the 2013 AL Division Series.
He refractured his medial epicondyle during a simulated game March 10, after originally fracturing it in May while pitching for Triple-A Nashville.
Parker's previous revised UCL did not need repairing, and the avulsed medial epicondyle fracture was cleaned up and repaired.