Kershaw was 15-2 with a 2.07 ERA before Sunday's game and even had a case for Most Valuable Player for the National League West-leading Dodgers. He threw 21 pitches and struck out two and walked one before manager Dave Roberts visited the mound.
Kershaw was removed from the game with back pain.
"Obviously, I'm not optimistic because I got taken out of the game," said Kershaw, who spent more than two months on the disabled list in 2016 with a back injury. "At the same time, some of the symptoms aren't as bad as they could be."
Kershaw said he was feeling "a lot of frustration" because his hundreds of hours of treatment and rehab apparently weren't enough to preserve his balky back.
The Dodgers, who lead the NL West by 10 1/2 games entering Monday, will not push Kershaw to return regardless of his recovery. At this point, Roberts expects a considerable stint on the disabled list for the team's ace.
Roberts would not comment on the team's interest in other starting pitchers. The Dodgers have been rumored to be interested in Texas Rangers right-hander Yu Darvish and have one week before the trade deadline.