Right-hander Chris Young will take Vargas' spot in the rotation on Sunday, while right-hander Edinson Volquez will move up a day and pitch Monday in Milwaukee. Right-hander Joe Blanton will pitch on Tuesday.
Vargas threw six shutout innings on Monday in Minnesota but felt the strain the next day. He tried to throw a side session on Friday and felt the strain still there. He then had an MRI on Friday.
"The tests just showed a little inflammation," manager Ned Yost said. "Everything else is in good shape.
"It may or may not have anything to do with this injury and (Yordano) Ventura's injury, but we've been hitting lately to play National League games."
"I don't think there's a lot of concern based on the results of the tests," Vargas said. "It's just something that flared up and having to get ready for a National League game and swinging the bat might have irritated it."
Vargas was on the disabled list in early May because of the same injury.
"It's a similar type strained feeling as before," he said. "It wasn't as intense."
Jeffrey Flanagan is a reporter for MLB.com. Follow him on Twitter at @FlannyMLB. This story was not subject to the approval of Major League Baseball or its clubs.