The Indians made the move before Monday night's game against the Chicago White Sox.
Aviles was originally put on the family medical emergency list, then was moved to the restricted list. His 4-year-old daughter, Adriana, has leukemia and was being treated at the Cleveland Clinic.
In 18 games, Aviles is hitting .288. He is hitting sixth and playing third base.
The Indians sent right-hander Austin Adams to Triple-A Columbus. He has a 1.59 ERA in three games.
Also, first baseman Carlos Santana was a late scratch because of back spasms.