Cashner, on the disabled list since April 6 with a strained right rotator cuff, was scheduled to have thrown two innings in Mesa, Ariz.
When Cashner returns, he will be inserted back into the rotation.
"Cashner's a starter, and that's what we're committed to," Cubs manager Mike Quade said.
Randy Wells, who has been on the disabled list since April 6 with a strained right forearm, will make a Minor League rehab start on Tuesday with Class A Peoria, and if all goes well, his next start would be on Sunday for Triple-A Iowa. If he passes all the tests, Wells could be back with the big league team next week.
Meanwhile, Doug Davis, who made his first start for the Cubs on Saturday, was not with the team in Cincinnati so he could be with his wife, Chantelle, who gave birth on Sunday. Davis' next scheduled start will be Friday against the Red Sox.
"He gave us five pretty good innings -- go have your baby and we'll see you in Boston," Quade said.