"He's been experiencing a little shoulder soreness. ... It's slight right now, and we want to keep it that way," Royals manager Ned Yost said.
Yost revealed Davis' problem after the Royals' game against the Indians was called off Friday in the third inning because of rain.
Davis almost certainly will make his next start on schedule in the next five or six days, Yost said.
"He still has a little inflammation," Yost said. "It started out with some tightness and inflammation in his shoulder and it progressively got better and better. We threw him on the side two days ago to gauge whether he could still make his start and he still felt it a little bit. And it didn't make any sense to go ahead and push through that."
In his previous two outings, Davis had not given up a run in five innings and was credited with victories in both games. He had surrendered three hits with three strikeouts and no walks (he hit one batter).
Davis came to the Royals along with James Shields in the major trade with the Tampa Bay Rays that cost the Royals four top prospects, including prized outfielder Wil Myers and pitcher Jake Odorizzi.
His sore shoulder marks the first setback for the Royals' rotation, which is to include Davis, Shields, Ervin Santana, Jeremy Guthrie and probably either Bruce Chen or Luke Hochevar.
Dick Kaegel is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.