Outfielder Tyler Naquin, who was on the IL since May 11 with a strained left calf, was activated prior to Tuesday night's game against Minnesota.
Rodriguez, who is 1-5 with a 4.74 ERA in eight starts, was removed after four innings Saturday against the Chicago White Sox. An examination showed a strain behind the shoulder and Rodriguez is expected to be shut down from throwing for at least two to three weeks.
Naquin began the season with the Indians and batted .278 with a home run and 10 RBIs in 30 games. He hit .304 with three homers and six RBIs in six games on a minor rehab assignment.