The rest of the rotation will also move up, meaning that left-hander Bruce Chen will start against the Orioles when the Royals' homestand opens on Tuesday night at Kauffman Stadium.
Davies isn't certain if he'll miss more than one start, pending an examination by doctors and an MRI on Monday in Kansas City. Earlier this season, Davies missed 6 1/2 weeks.
"It's the same thing that happened before, the shoulder inflammation," Davies said. "It was bothering me before the game in Boston that whole week and it hasn't gotten much better."
Last Monday night at Boston, Davies held the Red Sox to one run in six innings and the Royals won, 3-1, in the 11th. It was one of his best performances this year, even though he felt he couldn't fully extend himself in his delivery.
"Maybe it tells something," Davies said. "Maybe I don't have to overthrow the ball to get people out. It could be a learning experience but, obviously, I have to get my shoulder healthy."
Davies didn't want to risk starting on Sunday against the Indians and perhaps have to leave the game in the first inning or two.
"I want to make sure I can go out there and pitch six innings from the get-go and not have what happened against Cleveland the last time, where I had to come out after one-third and tax our bullpen again," Davies said.
On May 16, Davies left after one-third of an inning and the Royals had to use seven relievers in a 19-1 loss to the Indians. After that he was on the disabled list until July 2.
Manager Ned Yost went to a six-man rotation, instead of the usual five, when Davies returned so that rookie Duffy could stay in the mix.
"It's on a regular five-man rotation," Yost said on Sunday after announcing that Davies was scratched.