"Whatever Donnie said is what we'll go with," said Kershaw, referring to manager Don Mattingly, who said the first the club heard about the injury was Tuesday.
Kershaw will miss Sunday night's game with the Padres.
"I really wanted to pitch," he said. "I just had to admit I don't feel right. When they laid it out to me, we have guys who can fill in the spot, and with off-days, I'll just push back a few days and not miss a start."
That indicates Kershaw intends to pitch the Dodgers' home opener against the Giants on April 4, which also could mark the return of Matt Kemp from the disabled list.
"It's probably nothing I'm too worried about; it's frustrating more than anything because of the timing," he said. "If I had to pitch tomorrow, I'd do it, I wouldn't feel great."
Mattingly said he was concerned "obviously enough to be careful. It's the beginning of the season. Reason to be overly cautious. We don't want to let it turn into something longer."
Kershaw said he "didn't think" the compressed Spring Training, necessitated by the trip to Australia, "had anything to do with" his injury, nor did the long flight.
"I don't know how I did it," he said. "It's better each day, better today than yesterday. I think it's progressing well. I hope with an extra day it's good to go."
He said he did not receive an injection and that the primary therapy is "just rest." He said he would resume playing catch Friday.
He said he feels the discomfort when he brings his arm forward "accelerating."
One of the key reasons the Dodgers were willing to sign Kershaw to a seven-year, $215 million contract this winter is his durability. He's never been on the disabled list. He has missed a start because of a sore hip, but otherwise has been an iron man, making at least 30 starts each season since 2009. The only significant injury he's had is a separated right shoulder, incurred slamming into the fence shagging flies during batting practice in 2009.
But having pitched deep into October last year, including once in the playoffs on short rest, there had been internal concern about how much Kershaw should pitch this soon into the year. It was conceivable that, because of days off and travel, he could have started three of the club's first six games, but Mattingly repeatedly cautioned that it wasn't likely. He made 86 pitches in his final Cactus League start March 15. Mattingly indicated that Hyun-Jin Ryu or Dan Haren were the most likely candidates to make that start. Ryu reported improvement from the torn right big toenail, which was partially removed in a procedure Tuesday.
Kershaw is the latest Dodgers starting pitcher with an ailment. Josh Beckett, who threw a simulated game Wednesday night, is on the disabled list with a bruised hand. Chad Billingsley is recovering from Tommy John surgery. Ryu has the torn toenail, and Zack Greinke had a strained right calf muscle.
Mattingly said Greinke would start Tuesday night's game against the Padres. Monday is an off-day. Greinke will pitch Thursday in an exhibition against the Angels and will be pitching on normal rest against the Padres.
Ryu, who suffered his injury running the bases in Sunday's win in Australia, said he was dramatically improved after undergoing the procedure Tuesday to remove half of the nail. He practiced his delivery on the bullpen mound during Wednesday's workout and told the club he believes he will be able to land on the right foot by Sunday night.
If Ryu is unable to start Sunday night, it likely would be Haren, with Paul Maholm available to start in place of Haren on Wednesday.
Ryu predicted that his toe will heal quickly based on the improvement from the procedure. Because a Sunday start would be only eight days after his previous start, Ryu said he probably wouldn't need to throw a bullpen session. He rarely does when pitching on normal rest.