General manager Chris Wallace announced Thursday's procedure was performed at the Campbell Surgery Center by team physician Dr. Fred Azar and Dr. Drew Murphy.
Arthur, who was hurt on December 18, is expected to be ready for the start of the 2012-13 campaign.
The 23-year-old Kansas product averaged a career-high 9.1 points and 4.3 rebounds in 80 games last season. He contributed 7.1 points and 2.2 rebounds during the playoffs.
Arthur owns career averages of 6.9 points and 4.2 rebounds in 188 career games, all with the Grizzlies.