Puig, who is hitting .265 with 11 home runs, was removed from Sunday's loss to the Los Angeles Angels during a fifth-inning at-bat. Earlier, Puig homered for the second consecutive game.
Dodgers manager Dave Roberts said Puig might not return until August.
"It's going to be a few weeks," Roberts said. "With the time we have left in the season, we have to be very careful. Otherwise it can come back to bite you at an important time. So we are going to be patient."
Andrew Toles, who was out for two months with a hamstring injury, was recalled from Triple-A Oklahoma City. He was batting .326 in 34 games in the minors.