Anderson, who went 2-5 with a 6.68 ERA in nine starts this season, was bothered by pain in his elbow late in the year. The team said he was diagnosed with impingement in the back of the elbow joint.
The 26-year-old underwent an arthroscopic procedure in Dallas on Wednesday. The team said Anderson will begin a throwing program in two months and is expected to be ready for the start of the 2017 regular season.
Coming off an impressive rookie season, Anderson won a spot in Cleveland's starting rotation in spring training, but struggled in April and May. He spent most the season bouncing back and forth between the Indians and Triple-A Columbus. Anderson had seven stints with Cleveland.
Anderson was used exclusively as a reliever in the second half by manager Terry Francona.