Smith has been sidelined with an abdominal strain suffered during spring training. The club announced the move Friday before opening a three-game series against the Baltimore Orioles.
On Thursday, the Indians optioned reliever Frank Herrmann to Triple-A Columbus to make room for the side-arming Smith, who had a 3.60 ERA in five appearances during the exhibition season.
Smith went 2-2 with a 3.83 ERA in 53 games last season for the Indians. This is the 27-year-old's third season with Cleveland after coming over in a 2008 trade from the New York Mets.