The three-time Cy Young Award winner has left forearm discomfort, the same injury that sidelined him for 57 games from Aug. 9 to Sept. 13.
He worked out in the weight room Saturday and was still experiencing soreness, manager Dave Roberts said. Kershaw will undergo tests on Monday.
Asked if Kershaw will pitch again this season, Roberts replied, "I don't think so. There's always a chance, but right now where we're at, we're going to proceed with that mindset."
Kershaw left his start Friday night against Milwaukee after 1⅔ innings. He gave up three runs with one strikeout. He is is 10-8 with a 3.38 ERA, his highest mark since a 4.26 ERA as a rookie in 2008.
Roberts said he knew the potential existed for Kershaw to get hurt again.
"He was determined to do everything he could in his power to see everything through this year," the manager said. "Unfortunately, it gave way."
A subdued Kershaw knew immediately that his chances of pitching again this season were slim.
"I just wanted to be a part of this team going through October," he said. "This team is special."
Kershaw's injury moves left-hander Julio Urías into a starting role in the postseason, Roberts said.
The Dodgers went into Saturday two games behind San Francisco in the chase for the NL West title but assured of hosting the NL wild-card game if they don't catch the Giants with two games left.
The team recalled right-hander Mitch White.