"I just felt something grab and [in the third inning] I could feel it slowly and slowly getting tighter," he said.
Kennedy left the game after 33 pitches, having allowed two hits and two walks with two strikeouts in 2 1/3 innings. He was replaced by reliever Odrisamer Despaigne, who retired all 14 hitters he faced.
"This could be a possible disabled list [stint]. It's a mild hamstring strain. Those are tricky. Our doctors have looked at him," said Padres manager Bud Black. "Ian is a pitcher who uses his legs a great deal. It was affecting him through his warmups. We decided to make that move."
Kennedy hasn't had much of an injury history, as he's been on the disabled list once since 2009, and that was for a cut finger. Last season, Kennedy made 33 starts and led the team with 201 innings.
"It's frustrating, I was feeling pretty good," Kennedy said. "But I needed to stop. I wasn't pitching with the same effort because I was trying to protect [the hamstring]."
Black said that if a disabled list stint is needed, Despaigne will slide into Kennedy's spot in the team's starting rotation when it rolls around on Tuesday at home against the D-backs.
Corey Brock is a reporter for MLB.com. Keep track of @FollowThePadres on Twitter. This story was not subject to the approval of Major League Baseball or its clubs.