The Dodgers announced later Sunday that an MRI confirmed the original diagnosis of biceps tendinitis, meaning Kershaw will begin his rehab Monday. But the team has not disclosed how long it will be without the three-time Cy Young Award winner.
"It's [a] little bit head-scratching, but we have to keep moving forward," Dodgers manager Dave Roberts said. "I know he's frustrated, because he wants to carry the load."
Kershaw did not speak with reporters Sunday before leaving for Los Angeles. Roberts told reporters before the game that the Dodgers were "cautiously optimistic" about Kershaw, who started feeling discomfort while playing catch Saturday.
"I got word from the training staff yesterday when he was trying to play catch that it just was not feeling right," Roberts said. "He said that during his last start he felt it just a little bit, and we gave him a couple of extra days."
This is the third straight season Kershaw has been placed on the DL. He was put on the DL for five weeks in 2017 with a back strain and missed more than two months in 2016 because of a herniated disk in his back. Before that, he had only one DL stint (in 2014, for an inflamed back muscle) from 2008 to 2015.
Kershaw's latest trip to the DL comes at an inopportune time for the Dodgers, who already will have to play the rest of the season without injured All-Star shortstop Corey Seager.
Starting third baseman Justin Turner, a key cog in Los Angeles' lineup, hasn't played this season because of a broken left wrist but is expected to return later this month. Left-hander Hyun-Jin Ryu, the team's top starting pitcher this season, will be out until after the All-Star break with a severe groin injury.
"Obviously, it's been tough, but injuries are part of the game," Dodgers general manager Andrew Friedman said, according to MLB.com. "And we've seen this team respond to adversity in years past when others had written us off. And we expect to do the same thing."
Hill, who has been on the DL since April 18 because of a cracked fingernail, will be activated Tuesday to take Kershaw's spot in the rotation against the Diamondbacks.
Kershaw is 1-4 this season despite a 2.86 ERA and 48 strikeouts in 44 innings. His four losses are as many as he's had in both of the past two seasons (18-4 in 2017; 12-4 in 2016). Including the playoffs, he has pitched 2,101 innings in his career.
Kershaw is earning $30.4 million this year in the fifth season of a $215 million, seven-year contract, but he has the right to opt out after the World Series and become a free agent, giving up salaries of $32 million next year and $33 million in 2020.
Los Angeles recalled right-hander Brock Stewart from Triple-A Oklahoma City to take Kershaw's place on the roster Sunday.
ESPN Stats & Information and The Associated Press contributed to this report.