"Our plan wasn't to activate him on Tuesday anyway," Yost said. "Our plan was to give him until the end of the next rotation [Saturday] to see how he feels then. Give him the extra time there."
Kennedy's spot in the rotation on Sunday will be filled by Chris Young. That spot will come up again next Saturday.
Kennedy threw a bullpen session on Friday.
"He felt all right," Yost said. "He still felt a little tugging, which [trainer] Nick [Kenney] said would be normal. So he's making progress."
Yost said Kennedy may throw a light bullpen session again on Sunday or Tuesday.
Gordon sits with groin tightness
Royals outfielder Alex Gordon was not in the starting lineup on Saturday against the Orioles after being removed for a pinch-hitter in the seventh inning because of right groin tightness on Friday night.
"He's feeling better," Yost said. "We'll see how he feels tomorrow.
"I told him if he even feels the slightest bit of it tomorrow, we'll wait through the off-day [on Monday]. It's more of a precaution. It felt better today. If he doesn't feel it at all, we'll go ahead [and play him], otherwise Tuesday [against the Yankees] for sure."
Jeffrey Flanagan has covered the Royals since 1991, and for MLB.com since 2015. Follow him on Twitter @FlannyMLB. This story was not subject to the approval of Major League Baseball or its clubs.