After the game, Kennedy said he probably was being a bit overly cautious, mainly because an injury to the same left hamstring derailed his 2015 season to some degree.
But Kennedy said at this point, he didn't think his Tuesday start would be in jeopardy.
"No, I don't think so," Kennedy said. "I'm not too concerned ... I just wanted to be careful."
Kennedy said it felt more like a cramp than tightness.
"Maybe not enough water, or too much coffee," Kennedy said, smiling.
Kennedy logged three innings, allowing three hits and two runs while striking out four. He threw 43 pitches.
Yost said he will wait 24-48 hours on Kennedy's condition to see if he needs to make any adjustments to the rotation in the event that Kennedy might have to miss Tuesday's start. Yost mentioned Yordano Ventura, who is scheduled to throw briefly in Saturday's exhibition game against the D-backs, as a possible replacement.
"We'll wait to see if we have to adjust Yordano's throwing schedule," Yost said.
Ventura is scheduled to pitch on April 8 against the Twins.
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.