The designated hitter and first baseman, who turns 35 next month, hopes to return around the All-Star break. His procedures to repair loose cartilage in the knees were performed by team orthopedist Dr. John Frazier.
"Everything went well," A's manager Bob Geren said.
Sweeney also had right knee surgery last year in the final of his 13 seasons with the Kansas City Royals. Once swelling has subsided in both his knees, he'll spend a couple of weeks rehabilitating in San Diego with a therapist he's worked with before.
"They did the same thing to both," Oakland athletic trainer Steve Sayles said. "It was exactly what we thought. We're going to set it at four-to-six weeks."
Sweeney had another MRI exam on his right knee Monday and that showed further cartilage damage in the knee, leading to him having operations on each. His left knee hadn't responded to treatment since he went on the disabled list May 30 retroactive to a day earlier with inflammation in the knee.
Sweeney, who was batting .292 with two home runs and 12 RBIs in 40 games for the A's, had a cortisone shot June 2 and then a gel shot last Friday but neither helped alleviate the discomfort he felt.