The team made the announcement before Wednesday's game against St. Louis. Aviles was placed on the family emergency medical leave list last Friday.
Aviles visited Progressive Field, spoke with manager Terry Francona and worked out with teammates. Aviles might rejoin the Indians this weekend in Texas, but Francona said he will be given all the time he needs to be with his family.
Aviles' stay on the family emergency medical leave list will end Thursday. He could be moved to the restricted list if he isn't ready to rejoin Cleveland.