Drew was originally penciled into the Red Sox lineup for Friday's game against the Blue Jays, but was removed as his condition worsened during the day. It was the fourth straight game that the right fielder has missed because of back spasms.
Drew visited Toronto's Mount Sinai Hospital, where he underwent the tests.
"I had a good day yesterday," Drew said, after arriving at Rogers Centre on Friday. "I thought everything was going well. I don't know if it was the way I slept last night, but I got up today and it was stiff again."
The 32-year-old Drew has dealt with back woes at various points in his career. This year, there have been multiple occasions where his back has locked up on him, the first time coming just moments before Opening Day in Japan.
"For whatever reason, my back is really guarding against letting that spasm out," said Drew. "It's tough, because when I sit down and get relaxed, I try to stand up and then I'm stiff and it's hard to get moving."
Drew was asked if there is a chance he could end up on the disabled list.
"I'm hoping not," he said, noting that when the problem has occurred this season, it has only lasted for a few days at a time. "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."
For now, Drew is not partaking in any baseball-related activities. He is taking anti-inflammatory medicine and receiving treatment in hopes of calming his back down.
Francona also gave an update on the condition of shortstop Julio Lugo, who recently suffered a setback during his recovery from a strained left quadriceps.
"He actually doesn't feel too badly," Francona said. "It didn't get worse, but he's not going to go back there and resume [any running activities]. He's going to do the treatment. His range of motion was good. But you're not going to see him out there taking grounders.
"It's definitely a setback, but how far of a setback, I don't know."
David Singh is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.