Manager Don Mattingly gave the start to Joe Blanton, who was told late Saturday he had a 50-50 chance of starting Sunday.
Kershaw, who made his regular bullpen session Thursday, said he wasn't sure how the discomfort started. It began with referred pain in the groin, a common symptom of hip trouble.
"It just came on," he said. "Tweaked it somehow. It was enough that I wanted to get it looked at, make sure it's nothing serious. It feels better today."
Mattingly said the medical opinion was that, by giving the medication a few days to work (Monday is a day off), it would give Kershaw the best chance of getting through the season without missing another start.
"None of it made any sense for him to pitch today," Mattingly said.
He also said Kershaw would have started if it was the seventh game of the World Series, "no question." As big as Sunday's game was, Mattingly said, improving chances that Kershaw would remain healthy outweighed the one game.
"I want him to be in the best position to pitch the rest of the year," Mattingly said. "We have 20-something games left. Obviously, it is a big game; if we win it's a two-game swing, puts pressure on St. Louis or whoever's in front. But this is all about his best chance to be healthy the rest of the way."
Mattingly said John Ely or Stephen Fife could start Tuesday if Kershaw were unable to go.
Falsone said the medical department wasn't comfortable letting Kershaw pitch, even though he lobbied to.
"We're the bad guys," she said. "We didn't feel comfortable for 60 or 70 pitches. He got the cortisone injection, we'll let the medicine work."
Mattingly said the hip hasn't been an issue this year for Kershaw, who has 199 2/3 innings pitched. Falsone said it's not unusual for a pitcher's landing leg to develop soreness because of the rotational forces, but it generally dissipates.
"For whatever reason," she said, "it didn't go away this time around."