Kershaw consulted with team physician Neal ElAttrache, who reviewed an MRI scan and recommended Kershaw be placed on a rehab that includes a submaximal throwing program during that time frame.
He will then be re-evaluated to determine when he can start throwing at increased velocity. The team said there is still no time table for Kershaw's return beyond the two to three weeks.
Dodgers manager Don Mattingly said Kershaw will need to begin a throwing progression that would culminate in a minor league rehab assignment before the team would feel comfortable using him to pitch in a major league game.
Kershaw originally was scheduled to play catch before Tuesday's game in San Diego, but trainer Stan Conte scratched that because of the damp, chilly weather.
"He's definitely far enough out now that he's going to have to have some kind of progression," Mattingly said. "In my mind, it's going to take some time."
ESPN's Buster Olney reported that Kershaw's injury, which the team is describing as inflammation in the upper back, is similar to an injury the Padres' Andrew Cashner had two years ago. Cashner missed two months with it.
Kershaw pitched 6 2/3 strong innings on Opening Night in Australia March 22, but felt some tightness in his back upon returning to Los Angeles and was put on the DL Saturday.