Kershaw will be replaced by Joe Blanton, pitching on his usual four days' rest.
Dodgers manager Don Mattingly said Kershaw now is scheduled to start Tuesday night in Phoenix against the Arizona Diamondbacks, but the Dodgers will have either John Ely or Stephen Fife standing by if Kershaw can't go.
"Today, he felt like he could pitch. He's probably irritated with me," Mattingly said. "I think all the medical people feel this is the best chance of him being healthy the rest of the way."
Kershaw first experienced discomfort Friday. He had an MRI Saturday, which turned up inflammation in the hip.
"Right now, he's pitching Tuesday unless he gets out there and warms up or, between now and then, comes and says, 'This thing's getting worse,'" Mattingly said.
Kershaw also has been dealing with plantar fasciitis in his right foot for most of the season. He threw several warmup pitches from the mound at AT&T Park on Sunday afternoon shortly before the change was made.
"I felt good enough to pitch today," Kershaw said. "It's been in there for a few days. I got all that stuff done yesterday to make sure it was nothing serious."
The Dodgers, fighting to stay in the playoff race, already are without their best player, Matt Kemp, who is out until at least Tuesday after receiving a cortisone injection in his left shoulder. Kemp said his shoulder felt about the same Sunday as it had before and he doesn't know when he'll be back in the lineup.
"It's kind of day-to-day," Mattingly said.