The Royals announced that the move is retroactive to July 27. The team recalled left-hander Matt Strahm from Double-A.
Davis returned to Kansas City from Arlington, Texas, on Saturday night for an MRI on his right arm.
Manager Ned Yost said it's the same injury that sent Davis to the disabled list in early July.
Davis has converted 21 of 23 save opportunities in 35 appearances this season with a 1.60 ERA. In his most recent outing Wednesday, Davis allowed three walks for the first time as a reliever.
"Hopefully, he'll be back around the end of the 15 days," Yost said.
Strahm, 24, was moved to the bullpen recently after making 18 starts. Splitting last season between Class A Wilmington and Class A Lexington, Strahm had a 2.59 ERA and 121 strikeouts in 94 innings.
On Thursday, Kansas City placed right-handed reliever Luke Hochevar on the disabled list with symptoms of thoracic outlet syndrome.
Davis also has been mentioned in trade rumors with the non-waiver deadline approaching Monday.
Information from The Associated Press was used in this report.