"I'll probably be a couple of days just to get things under wrap," he said.
Drew injured his hamstring while catching Manny Ramirez's line drive in the third inning Friday night and left the game. He had an MRI on Saturday and was awaiting the results.
"I don't think I've done an extreme amount of damage," Drew said. "I went to get a couple of pictures just to make sure."
Bill Hall started in right field for the Red Sox. Boston manager Terry Francona said Drew won't play Sunday, either.
Drew is hitting .276 with eight homers, including one in Friday's win over the Dodgers, and 37 RBIs.