Francisco initially had an MRI performed on Friday but the results came back clean. He felt some discomfort while throwing a bullpen session on Saturday, though, and the club is opting to send him for another examination.
Toronto was hopeful that it would take place on Monday but there weren't any flights available to Birmingham, Alabama, where Andrews is based.
"I think more than anything this is to give us as much information as possible to give him peace of mind and just make sure there's nothing in there," Blue Jays manager John Farrell said. "We have every reason to believe there isn't, to date, because of the MRI we've received, so there's no structural issues.
"But we just want to be sure we do the right thing by Frankie and get him checked out by Dr. Andrews."
Right-hander Octavio Dotel is set to appear in a Minor League game on Tuesday as he attempts to return from a right hamstring injury. Toronto would like to find out by Wednesday whether he will be ready for Opening Day.
"That's probably a pretty good mark on the calendar," Farrell said. "Are we going to be able to factor them in for Opening day -- I think as we get to the middle of the week [we'll know].
Farrell's use of the bullpen on Sunday afternoon against the Twins could act as a prelude of what to expect at the start of the regular season.
Right-hander Jon Rauch closed out Toronto's 3-0 victory with a scoreless ninth inning. Jason Frasor threw a scoreless eighth while Shawn Camp accomplished the same feat in the seventh inning.
If Francisco and Dotel require time on the disabled list Farrell indicated that that is the formation of the bullpen he prefers.