The lefty will meet with Dr. Bryan Kelly in New York on Tuesday for a second opinion and, based on persistent symptoms, he may need surgery for a labral tear. Teammate Jerry Hairston underwent a similar surgery in Vail, Colo., on Monday that requires three to five months to recover.
In the meantime, manager Don Mattingly is waiting for the news before committing to a rotation down the stretch.
"We'll just see," he said. "That is all going to be up in the air."
Chad Billingsley, who was pitching lights out in the second half, is already done for the season with a sore right elbow, and Ted Lilly has been out since May with surgery coming.
The uncertainty about Kershaw and injuries to the rotation moves newly acquired Josh Beckett into the role of staff ace.
"For the most part, you've got to look at Josh," said Mattingly, who added he will go with whoever matches up best if the time comes. "I think we have to. He's the guy that has pitched the most big games, but our guys have all thrown the ball pretty well.
"[Chris Capuano] has probably struggled as much as anybody the second half, but he's capable of going out and throwing zeros for us."
Beckett is 7-3 with a 3.07 ERA in the playoffs through 14 games and 13 starts with a World Series MVP on his resume.
After posting a 5.23 ERA and 5-11 record with the Red Sox this season, Beckett has looked good since joining the Dodgers. He's 1-2 with a 3.38 ERA in four starts.
Rookie Stephen Fife started Sunday in Kershaw's place, and Mattingly said he would likely go with a four-man rotation if the days off permit.
Mattingly promised he wouldn't pitch Kershaw this season if there's any chance of further damage, no matter the game.