The Dodgers are hopeful the strain is mild, but Kemp missed 51 games -- spanning two DL stints -- with a strained left hamstring in 2012.
"I don't want to be in the same situation where I come back, hurt it again and sit out another month," said Kemp, who is in the second season of an eight-year, $160 million deal. "That's just not what I want to happen this year, so just kind of get it better now and, you know, be better."
Kemp hurt himself chasing Mike Trout's double to right-center field Wednesday night.
Kemp, a two-time All-Star, is batting .251 this season with two home runs and 17 RBIs in 51 games. He has struck out 60 times in 191 at-bats after offseason left shoulder surgery. In his past six games, he is 1-for-17 with 10 strikeouts.
"We don't feel like it's going to be three weeks or anything like that. With these things, you never know because they seem to linger," Dodgers manager Don Mattingly said. "But he'll be able to work on his stroke and do some things as time goes. It's hard to say you don't play for some days and actually get better, but it could be a fresh start for him."
The Dodgers plan to recall a center fielder to replace Kemp while he's out. They used right fielder Andre Ethier there as a stopgap Thursday.
Mattingly said the team isn't considering recalling either of its top position-player prospects, Yasiel Puig or Joc Pederson. The Dodgers likely will bring up Tony Gwynn Jr. from Triple-A Albuquerque this weekend.