Greinke started for the NL in the All-Star game and pitched two innings.
Manager Don Mattingly said recently that he didn't want Bolsinger and the team's fifth starter to continue pitching on consecutive days, as their inability to pitch into the later innings has burdened the bullpen.
Carlos Frias has been the fifth starter for the majority of the season but is currently on the disabled list.
Frias' most recent turn in the rotation was taken by Brandon Beachy, who returned from his second reconstructive elbow operation. Beachy lasted only four innings and was charged with three runs.