Smith, who typically starts against only right-handers as the designated hitter, hasn't been in the lineup since Saturday. He's batting .241 with six home runs and 33 RBIs on the season.
Alberto Callaspo, who has a pair of three-hit games in his last three contests, started at DH on Wednesday.
Jane Lee is a reporter for MLB.com. Read her blog, Major Lee-ague, and follow her on Twitter @JaneMLB. This story was not subject to the approval of Major League Baseball or its clubs.