Fellow right-hander Dustin McGowan was shut down for a week due to a tired arm, one day after pitching in a game for the first time in nearly 21 months.
Morrow, acquired from Seattle and projected to be Toronto's No. 3 starter, said he could have pitched Saturday against Atlanta if it was a meaningful game but decided to rest the shoulder for a few days.
"I don't want to turn what should be a two- or-three-day setback into a two-week setback by going out there and letting it get inflamed," he said. "I just wanted to back off, let it calm down a little bit. Better to do it now than in two weeks.
"I would have rather gone out there but I think they also appreciate the fact that I'm trying to be smart about it and trying to make sure I'm ready for the opening series rather than trying to pitch through stuff now."
Morrow said his shoulder felt "cranky" Wednesday after a bullpen session. Thursday and early Friday, he said, he felt fine playing catch in the outfield, but the discomfort returned "when I started to crank it up a little bit on the mound" before the start of the game against Houston.
"Just the right thing to do if you're feeling something," Blue Jays manager Cito Gaston said. "Here's a kid that we think is going to be a big part of this organization. Why risk the chance?"
McGowan last pitched July 8, 2008, against Baltimore, leaving the game with a sore right shoulder that required surgery. He sat out all of 2009 due to delays in rehabilitation, including right knee surgery.
On Friday, he threw 36 pitches over 1 2/3 innings Friday in a minor-league game and said his arm was "worn out."
He will start the season on the disabled list. Gaston said trainer George Poulis told him that McGowan may just have a dead arm right now because he has been throwing since November.
"You just hope that's what it is," Gaston said. "He'll rest for seven days and if we can get him back a month into the season, whenever we can get him back will be great."