Kershaw complained of tightness during a workout on Tuesday and an MRI showed inflammation in a back muscle.
The team said Kershaw's next start would be determined by his progress with his throwing during the next week. Dodgers manager Don Mattingly did not name a starter for Sunday, but says Zack Greinke will get the start on Tuesday.
The Dodgers pitching staff is dealing with a myriad of injuries, with Chad Billingsley recovering from Tommy John surgery, Josh Beckett on the disabled list with a bruised hand, and Hyun-Jin Ryu dealing with a torn toenail.
Kershaw earned a victory in the Opening Day game against the Arizona Diamondbacks in Australia last weekend, pitching 6.2 innings, allowing five hits and one earned run while striking out seven in 102 pitches.
Kershaw, last season's National League Cy Young award winner, agreed to seven-year, $215 million deal in January. PHOTOS: MLB's 2014 Team Payrolls