Chafin is 5-1 with two saves and a 2.41 ERA in 55 appearances and 67 1/3 innings this season.
It is his first full year in the majors, and he is eligible to return to the Diamondbacks when the minor league season ends for Reno on Sept. 7.
"We've run him hard this year, first year being a reliever," Diamondbacks manager Chip Hale said before Sunday's game against Oakland. "He's logged the most innings of a rookie reliever this year, so we just need to give him a break. He'll be back when he's eligible to come back."
Hale said the 25-year-old Chafin is a little tired.
"We need to be vigilant on taking care of our arms," Hale said. "I told him he's probably one of the brightest surprises on the team this year. He understood. I don't think he's OK with it, which is to be expected."
The Diamondbacks promoted pitchers Allen Webster and A.J. Schugel from Reno and Silvino Bracho from Double-A Mobile. Webster made his fifth start for the Diamondbacks on Sunday, Schugel is in the majors for the second time this season, and Bracho is coming off an impressive performance in the minors.
Bracho, 23, was 2-1 with 19 saves combined at Class A Visalia and Double-A, with 71 strikeouts and 10 walks in 42 games. Opponents batted .181 against him in his final 24 appearances.