In two rehab outings with Class A Advanced Visalia, the 30-year-old righty threw two scoreless innings with one hit and three strikeouts.
"He wont be back at least until after the weekend," manager Chip Hale said on Wednesday.
Asked whether Hernandez would need to go back-to-back days before joining the Major League club to see whether he could handle the workload, Hale said no.
"I think that's something we talked about, but I don't think we do," Hale said. "I think we can do it up here if we had to after he had a few outings. I think we could give him every other day for a while until we're ready to do that."
Depending on how the weekend goes will determine if Hernandez follows the team next week. After the D-backs close out their seven-game trip with Thursday's matinee in Miami, they return to Arizona for a series with the Cubs before going out on the road for another six contests.
From 2011-13, Hernandez recorded 17 saves and 63 holds with the D-backs. His experience in the late innings should boost the staff, which entered Wednesday with a 4.43 ERA in the seventh inning or later.
"I think he has to get a little bit of a soft landing here," Hale said. "I think everybody does. It's too hard. He had no Spring Training. His Spring Training has been extended spring with the affiliates. It's tough. I'd like to give him some outings where it's wasn't a huge amount of pressure, but you never know. I don't see him closing right out of the chute, but he's a guy once he gets on his feet, we know he's healthy, he feels good about his arm, he can be right in there."