Daniel Ponce de Leon replaced the 37-year-old on Friday night.
A three-time All-Star, Wainwright is 5-7 with a 4.31 ERA in 16 starts this season. The Cardinals did not put him on the injured list, and manager Mike Shildt said he could make his next start as early as Sunday.
Wainwright has a $2 million base salary and has earned a $500,000 bonus for making five starts and $1 million apiece for making 10 and 15 starts. He would earn $1.5 million for 20 and $2 million apiece for 25 and 30.
Ponce de Leon is 1-0 with a 2.16 ERA in three starts and three relief appearances this season.
The Diamondbacks started left-hander Robbie Ray, who is 6-6 with a 3.96 ERA.