The surgery was performed by team doctors Steve Lombardo and Dan Kharrazi of the Kerlan-Jobe Orthopaedic Group in Los Angeles.
World Peace, who has averaged 12.8 points, 5.1 rebounds and 1.70 steals in 70 games (64 starts) this season, is expected to be out a minimum of six weeks, putting his status for the remainder of the season in doubt.
World Peace had been the only member of the Lakers' season-opening starting lineup yet to miss a game because of injury this season before he was sidelined for Wednesday's contest against Minnesota.
World Peace left Monday's 109-103 loss to the Golden State Warriors with a strained left knee and did not play after halftime. When asked by reporters after the game, he could not remember the specific play that caused the injury but said it occurred late in the second quarter.
A 14-year veteran, World Peace had been enjoying a renaissance season, as his points, rebounds and steals per-game averages, as well as his field goal percentage, 3-point percentage and free throw percentage, were all up from last year.
In Wednesday's 120-117 win over the Timberwolves, Lakers coach Mike D'Antoni adjusted his starting lineup, going with a three-guard lineup that included Jodie Meeks replacing World Peace.
Entering Thursday's games, the Lakers (37-35) have a one-game lead over Utah for the eighth and final playoff spot in the Western Conference with 10 games remaining.
Information from ESPNLosAngeles.com's Dave McMenamin was used in this report.