The procedure was performed by head team orthopedist Dr. Peter Asnis at Massachusetts General Hospital, and Kimbrel is expected to miss three to six weeks while recovering.
Kimbrel, acquired in an offseason trade with San Diego, sustained the injury while catching fly balls in the outfield during batting practice before last Friday's game against Houston.
The 28-year-old flamethrower was placed on the 15-day disabled list Saturday with a left knee medial meniscus tear.
Kimbrel, named an All-Star for the fifth time in his career, is 1-3 with a 3.55 ERA and 17 saves in 34 appearances this season.
Toronto's Aaron Sanchez (9-1, 2.97 ERA) replaced Kimbrel on the American League All-Star roster for Tuesday night's Midsummer Classic in San Diego.