Miller, acquired in a blockbuster offseason trade with the Atlanta Braves, had been out since May 24 because of a sprained index finger.
On Monday, Miller (2-6) pitched 6 2/3 innings, allowing one run and five hits while striking out five as the Diamondbacks won 3-1. It was Miller's first start since May 24.
"I'm just trying to keep up with them,'' Miller said of the rest of Arizona's rotation. "They've been doing so good.''
To make room for Miller on the active roster, the Diamondbacks placed outfielder David Peralta on the 15-day disabled list with a lower back sprain.
Miller, 25, was off to a rough start in his first season with the Diamondbacks, with a 7.09 ERA over his first 10 starts.
Peralta previously had missed nearly a month with a wrist injury and only returned to the Diamondbacks less than two weeks ago. He said Sunday that his back felt "tight and sore" after taking some swings in the batting cage, prompting manager Chip Hale to acknowledge that a return to the DL was possible.
The Diamondbacks made a pair of other roster moves before Monday afternoon's game, optioning utility player Brandon Drury to Triple-A Reno and recalling outfielder Socrates Brito, who started in center field and batted sixth in the lineup.
Brito made two stellar plays on defense in Monday's victory, including a diving catch.