Manager Don Mattingly said Kershaw didn't sustain the injury in New York, rather in a between-starts bullpen session.
"I think yesterday he was a little tender. When I saw his face coming in, I knew," Mattingly said. "We thought he'd be ready to roll tonight, but yesterday wasn't that great. With [Bolsinger] on regular rest, and the off-day tomorrow, there's no reason to push it."
Moving Kershaw to Friday puts Greinke in line to start on Saturday. Sunday's starter hasn't been announced. Reports have indicated that the Dodgers are close to acquiring Mat Latos from the Marlins, and Los Angeles still has Zach Lee, who made his Major League debut last week, on the active roster.
• LA, Miami working on deal involving Latos, Morse
Kershaw missed a start in September 2012 with a right hip impingement that responded to treatment. When asked if this injury was similar to the one in the past, Kershaw was curt.
"I don't want to talk about last year or a few years ago," he said. "It flared up this time. I don't know why."
Relief pitcher Chris Hatcher threw a scoreless inning for Class A Advanced Rancho Cucamonga on Wednesday, recording a strikeout and allowing no hits in his third rehab outing.
The right-hander, who is 1-4 with a 6.38 ERA in 27 appearances for the Dodgers this season, has been on the disabled list since June 17 with a strained left oblique.
Steve Bourbon is an associate reporter for MLB.com. Ken Gurnick contributed to this report. This story was not subject to the approval of Major League Baseball or its clubs.