Drew left an Aug. 17 game with tightness in his lower back and missed all three games of Boston's recent series in Baltimore. He was expected to return to the lineup Friday but had to be scratched when the soreness returned.
"We've got to figure out and get to a point where I don't want to miss any more time. It could be better tomorrow, it could be better on Sunday," he said before the Red Sox played Toronto on Friday night.
Drew is batting .280 with 19 homers and 64 RBIs,
"For whatever reason, my back is really guarding against letting that spasm out," Drew said. "It's tough, because when I sit down and get relaxed, I try to stand up and I'm stiff and it's hard to get moving."
Drew, who has faced back pain throughout the season, went to Toronto's Mount Sinai hospital Friday where doctors diagnosed the herniated disk, prescribed a course of anti-inflammatory drugs and gave Drew an MRI exam.
In other injury news, Red Sox manager Terry Francona said right-handers Josh Beckett and Tim Wakefield will both throw in the bullpen Saturday, while infielder Julio Lugo (quadriceps) is not yet ready to begin a minor league rehab assignment.
Smith takes the spot of right-hander Clay Buchholz, who was demoted to Double-A Portland on Wednesday after going 0-7 with a 9.21 ERA in his past 10 starts.
Beckett allowed eight runs and eight hits in 2 1/3 innings in a loss to Toronto last Sunday, then woke up the following morning with numbness in right arm. Scheduled to face Toronto again Saturday, Beckett has been pushed back and will not pitch again until Tuesday at New York at the earliest.
Beckett, 11-9 with a 4.34 ERA in 23 starts, played catch Friday and reported no pain, Francona said.
"I don't think there were any complaints or anything," Francona said. "He actually threw the ball pretty well. We just want to make sure we do the right thing."
Wakefield, out since Aug. 7 with tightness behind his right shoulder, could return to face the Yankees if his condition continues to improve. The knuckleballer is 7-8 with a 3.67 ERA in 23 starts.
Lugo, batting .268 with one homer and 22 RBIs, went on the disabled list July 12 and had problems Tuesday, delaying his rehab stint.
"He actually doesn't feel too bad today," Francona said. "It didn't get worse, but at the same time, he's not going to go back out there and resume what he was doing. He's going to get treatment. His range of motion was good, but you're not going to see him running around and catching grounders, either. It's definitely a setback, how far of a setback, I just don't know."