Drew was not in the lineup on Wednesday afternoon, but Red Sox manager Terry Francona is confident that the left-handed hitter will return following Thursday's off-day.
"We have a day game, so let's not make something that's not terribly serious worse than it needs to be," said Francona.
The back is just something that flares up on Drew every now and again, often without warning.
Just minutes before Opening Day at Tokyo Dome, Drew had to be taken out of the lineup. In that case, he took close to a week to recover. This time around, the injury appears to be less severe.
Drew is slated to play in the All-Star Game on Tuesday at Yankee Stadium.
"It's not as bad as Japan, and that's in his words," Francona said. "But it was getting stiffer by the minute. Once we got the lead, we tried to get him out of there. We knew that we had a day game today, that he probably wouldn't play. We have a day game tomorrow, so let's not make something that's not terribly serious worse than it needs to be."
With Drew out of the mix, Manny Ramirez returned to left field, and Brandon Moss got the start in right. Sean Casey served as the DH. Ramirez had been used almost exclusively at DH in recent weeks because of a sore right hamstring.
What type of improvement did Ramirez show that enabled him to return to the outfield?
"[Because] J.D. is hurt," quipped Francona. "Kind of talked to him last night. We have a day off tomorrow. I kind of wanted to play him one or the other. Last night or today. And we had discussed that before. So now, with J.D., it makes it a little easier. We can get Casey's bat in the lineup."
Ian Browne is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.