Kemp will be evaluated on Wednesday and his status will be updated then, said interim manager Pat Murphy.
Kemp had an RBI single in the fourth inning, but Melvin Upton Jr. replaced him in the fifth inning in the first game of a three-game series against the Brewers.
"The other day I was swinging and it started irritating me a little bit and it carried over into the off-day [Monday] and into today. We'll get it looked at tomorrow and see what's going on," Kemp said.
"Every time I swing, it got irritated, a sharp little pain. I wanted to keep going, but thought it would be better for me to sit this one out."
Kemp has been very durable in his first season with the team.
Murphy said Kemp tried to talk his way into remaining in the game.
"[He] wasn't really able to grip the bat. He's been feeling it for a couple days, played through it, and now it's getting checked out," Murphy said. "We thought it was best to get him out of there."
Kemp went into the game on Tuesday 11th in innings played in the National League (1,277) and tied for seventh in games started (148).
After struggling in the first half of the season, Kemp has 53 RBIs in the second half and 29 extra-base hits.
"It's a step forward. I guess it's always good to drive in 100 [runs], but I'd rather have 80 RBIs and go to the playoffs. Hopefully, it's a step forward going into next year and we can win more games," Kemp said.
Corey Brock is a reporter for MLB.com. Keep track of @FollowThePadres on Twitter and listen to his podcast. This story was not subject to the approval of Major League Baseball or its clubs.