The Bears also agreed to terms with tight end Draylon Ross on a practice squad contract .
Adams, an undrafted rookie free agent out of Purdue, had primarily been a contributor on special teams.
The injury occurred while Adams was blocking on a field goal attempt in the Bears' 30-24 victory over the Philadelphia Eagles on Monday night.
Smith, an undrafted rookie free agent out of Virginia Tech, has spent the season on the Bears practice squad. Ross, an undrafted rookie free agent out of North Texas, spent part of training camp on the Bears roster in 2011.