The two-time Cy Young Award winner had an MRI on Wednesday that showed the swollen muscle in his left upper back. Kershaw had complained of tightness while throwing at a workout on Tuesday.
The team said Kershaw's next start will be decided by his progress while throwing in the next week.
The Dodgers open the North American portion of their schedule at San Diego on Sunday. They began the season with two victories over Arizona in Australia last week. Kershaw started the first game Down Under, winning 3-1.