"By the time we have the four all ready to play, we'll be a few weeks from the end [of the season]," general manager Ned Colletti said.
Dodgers manager Don Mattingly said Kemp would not be activated when he's eligible Aug. 6, and the club does not have a timetable for his return.
Kemp has only been able to hit off a tee and play catch since he was injured during an awkward slide at the plate July 21 vs. the Nationals.
"We were hoping this was going to be a simple ankle sprain, but it's a lot more serious than that," Mattingly said. "He's been able to do some things, but is having soreness with that. We're still not where we need to be."
Kemp has been on the disabled list three times this season and has been limited to 62 games.
Austin Laymance is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.