The Dodgers will officially determine how long Kershaw will be sidelined after the three-time Cy Young Award winner visits with the team's back specialist, Dr. Robert Watkins, the source confirmed to Crasnick.
Dodgers manager Dave Roberts later told reporters there is no timetable yet for Kershaw's return.
"If you look at the calendar, and you are talking about a strain -- him making an impact on our club this year is a very safe bet," Roberts said.
Kershaw left Sunday's game against the Braves after just two innings and was diagnosed with what the Dodgers referred to as tightness on the right side of his lower back. The Dodgers will place Kershaw on the 10-day disabled list; they have not officially disclosed a timetable for his return.
"He's doing OK under the circumstances," Roberts said. "One day you're starting a major league game, and the next day you're in shorts and a T-shirt kind of feeling like a man without a country. Going from the locker room to the training room and you're not active. So he's disappointed. He's frustrated because he put in a lot of work to get where he's at today. ... All players, once something happens they want direction, a plan of attack -- once he gets that I think he'll be in a better place."
The news was first reported Monday by Fox Sports.
Kershaw, who is 15-2 with a 2.04 ERA this season, said Sunday that he was feeling "some frustration" with his latest injury. He missed 2½ months with a herniated disk in his back last year.
"I don't want to compare, just because there's so many variables," Kershaw said Sunday. "I don't even know."
Roberts told reporters Sunday that he thinks Kershaw's injury is strictly muscle-related, adding that the All-Star left-hander didn't feel the shooting pain down his leg that is usually caused by a herniated disk.
The Dodgers (68-31) have the best record in the National League. They are 19-2 when Kershaw, 29, starts this season, including winning 15 in a row.
Information from ESPN's Alden Gonzalez and The Associated Press was used in this report.