Hawpe hit .231 with four home runs, 19 RBIs and had a .301 on-base percentage in 195 at-bats with the team.
Hawpe, who has been on the disabled list since June 21, signed a one-year deal for $2 million with a mutual option for 2012.
The option is for $6 million with a $1 million buyout.
The surgery was performed on Friday by Dr. Heinz Hoenecke and Dr. Daniel Keefe at the Scripps Clinic in Carmel Valley.
The surgery, commonly referred to as "Tommy John surgery" included reconstruction of the ulnar collateral ligament.
The recovery time, according to the team, is approximately nine months.
Hawpe was originally placed on the 15-day DL with a strained right middle finger, though his elbow had troubled him long before that.
Hawpe was the Padres Opening Day starter at first base. He hit .149 in April, though he bounced back to hit .303 in May. He then hit .205 in June before landing on the DL.