Miller allowed five earned runs and struck out five in 3 2/3 innings, taking the loss as the Diamondbacks fell 9-5 on the road.
Miller, who had Tommy John surgery last year, was making his first start in 14 months.
To make room for Miller, the Diamondbacks put righty Clay Buchholz on the 10-day disabled list. Buchholz, who is 2-1 with a 2.56 ERA in seven starts this season, left his Sunday start after five innings with side tightness.
Miller allowed 10 runs on 20 hits with 28 strikeouts and six walks in a combined 19 1/3 innings during his four rehab starts, two with Double-A Jackson and two with Single-A Visalia.
The Diamondbacks also announced that lefty starter Robbie Ray will start Wednesday in Miami.
Ray, who has been out since April with a right oblique strain, had been scheduled for another rehab start Monday. But that has been scrapped in favor of a quicker return to the team's major league rotation.