Love was injured in Cleveland's series-sweeping win at Boston on Sunday, and will miss the remainder of the NBA playoffs.
The team announced late Wednesday night that Love had the operation earlier in New York. The Cavaliers said Love's projected recovery time is four to six months.
Love was in his first season with Cleveland, which acquired him last summer in a trade from Minnesota. The six-year veteran struggled at times during a bumpy year with the Cavaliers.
On Tuesday, General Manager David Griffin said it was "highly unlikely" Love would return during the postseason.
Love can opt out of his contract this summer and become a free agent.