Kershaw allowed three hits and one run to the Oakland Athletics and retired eight of the nine batters he faced after getting hit.
Kershaw told reporters after the game that he chipped a tooth but was otherwise uninjured.
Kershaw, 27, won his second consecutive Cy Young Award last season and his third in four seasons. He also won the National League MVP.
Kershaw, who will start on Opening Day for the Dodgers, was 21-3 with a 1.77 ERA in 27 starts last season.
Earlier Friday, the Dodgers announced that Hyun-jin Ryu, their No. 3 starter, will be shut down for three days with inflammation in his shoulder.
- Dan Gartland