Ray had been lined up to pitch Friday, but the team will take advantage of the opportunity to give him an extra day's rest.
In five starts before going on the disabled list Anderson had a 9.12 ERA and the D-backs suspected he would benefit from some rest.
"There was some tightness in the tricep, there was some issues there," D-backs manager Chip Hale said. "But I think you're exactly right, I think it was more just the need to get him a break."
Hale said he was encouraged by the fact that Anderson hit 93 and 94 mph during his rehab start.
Other rotation adjustments could come next week when the D-backs will likely use Thursday's off-day to split up left-handers Ray and Patrick Corbin in the rotation.
It is also possible later this month that the D-backs could look to give Rubby De La Rosa or Ray a break from the rotation due to concerns about the number of innings they have been throwing.
"These guys are going to log innings they've never logged before," Hale said.
Steve Gilbert is a reporter for MLB.com. Read his blog, Inside the D-backs, follow him on Twitter @SteveGilbertMLB and listen to his podcast. This story was not subject to the approval of Major League Baseball or its clubs.