The plan is for Morrow to start the series finale against the Red Sox, but he's in Florida being evaluated and the club won't know more about his status until closer to Sunday.
"He was throwing his bullpen [session] and had muscle spasms in his upper back and the next day it moved up towards his neck," Toronto manager John Gibbons said. "Just have to get that out of there."
The Blue Jays can only hope that Morrow will be able to go because there aren't a lot of options at their disposal if he has to be scratched for a second time.
Josh Johnson and J.A. Happ are noticeable absences from the rotation as both are on the 15-day disabled list while left-hander Ricky Romero was optioned to the Minor Leagues after a poor outing on Wednesday versus Tampa Bay.
The intention is that Morrow will be able to take the mound, but there is skepticism that he'll be deemed ready to go. That's a natural reaction after Johnson and Sergio Santos were both said to have minor injuries until they lingered and required stints on the DL.
Morrow indicated on Thursday that he was feeling better, but the club is still taking a precautionary approach. If the discomfort lingers, the Blue Jays won't want to risk it turning into something more severe.
If Morrow does get scratched, Gibbons believes the club will find an internal candidate rather than making a trade this early in the season.
"I'll tell you, [general manager Alex Anthopoulos] never sleeps, he's always looking for different ways to make the team better, so I'm sure he's looking that route as well," Gibbons said. "But it's not easy to do, especially this time of year, teams don't want to give up players because most of them still think they have a shot as well.
"I would be very surprised if we ended up going that route if he couldn't pitch Sunday."
The injury comes at a less than ideal time as Morrow is coming off his best start of the season. He allowed just two runs over eight strong innings against the Mariners.
Morrow is 1-2 with a 4.69 ERA in seven starts this season. He has struck out 34 and walked 17 in 40 1/3 innings as the club's No. 2 starter.
Gregor Chisholm is a reporter for MLB.com. Read his blog, North of the Border, and follow him on Twitter @gregorMLB. This story was not subject to the approval of Major League Baseball or its clubs.