Reed went 0-1 with a 4.88 ERA for the Tigers. In his last 11 appearances, the right-hander posted a 7.71 ERA.
Manager Brad Ausmus says the move had nothing to do with Reed's legal situation. Reed faces a sexual assault complaint, though prosecutors have not yet said whether he will be charged.
Detroit purchased Smith's contract after he went 4-2 with a 1.64 ERA in 15 games for Toledo. He also made seven appearances with Double-A Erie.
The Tigers have lost 19 of their last 28 to fall out of first place in the AL Central - with their bullpen among the primary culprits for the slide.