The 37-year-old Arroyo, who signed a two-year, $23.5 million contract with the Diamondbacks on Feb. 7, was scratched from his start Tuesday after feeling discomfort while running during warm-ups. He had an MRI, which revealed a slightly bulging disk.
"[The doctors] just want it to calm down before he starts throwing again," general manager Kevin Towers told reporters Wednesday. "Of course, Arroyo doesn't think it'll take that long. We'll just have to play it by ear to see how he's feeling."
Added manager manager Kirk Gibson on Thursday: "We still feel like there's enough time for him to be ready for the beginning of the season."
Gibson said Arroyo could pitch in a minor league exhibition when he's ready to return to game action.
"I think he wanted to throw today, but I don't know that was in the cards. Maybe tomorrow," Gibson said before the Diamondbacks played Oakland. "Just kind of want to make sure we're on solid footing before introducing twisting in his back again. He's had this before. It's kind of resolving itself like it has in the past."
Arroyo has never been on the disabled list during a major league career in which he's surpassed 200 innings in eight of the past nine seasons.
The right-hander is 138-127 with a 4.19 ERA over 14 seasons with Pittsburgh, Boston and Cincinnati. He had pitched for the Reds since 2006, when they acquired him from the Red Sox in a trade for outfielder Wily Mo Pena, and was 14-12 with a 3.79 ERA and 124 strikeouts last season.
Right-hander Bo Schultz is scheduled to take Arroyo's turn in the rotation Sunday against San Diego.
Information from the Associated Press was used in this report.