Right-handed pitcher C.C. Lee was recalled from Columbus.
Salazar is 4-5 with a 4.88 ERA in 12 starts for Cleveland this season. He had won his past three starts before he allowed five runs on two home runs in four innings at Cincinnati.
The Indians want to give Salazar a break and strengthen the bullpen, manager Terry Francona said.
"We've got some off-days coming up. This will give him an extra day of rest," Francona said. "We're trying to cover a lot of things. We knew we wanted to give Danny a [rest], and this is the best time to do it."
Lee is 0-0 with a 4.26 ERA in 15 games with Cleveland this season.