That recently changed and Morrow has been cleared to start a throwing program with another rehab stint to follow at some point in July.
"Normally, when you look at a starter, they need at least three [rehab starts]," general manager Alex Anthopoulos said. "You have to build up to five or six innings and most times out, you're looking at two or three the first time. We think it'll be right around there."
Morrow is just one of several injured Blue Jays pitchers attempting to make their way back. Righties Kyle Drabek and Drew Hutchison are both making progress in their rehabilitation from last year's Tommy John surgery, but aren't expected to make an impact this season.
Drabek began a rehab assignment with Class A Dunedin and likely will be optioned to the Minors in the near future. Hutchison is still just taking part in simulated games, but he'll begin a rehab assignment soon before following a similar path as Drabek.
The same can't be said for left-hander Luis Perez, who also underwent Tommy John surgery last season. Perez began a rehab stint in early June, but suffered a setback when he experienced discomfort in his left elbow.
"Perez is doing better, he had a bit of a flareup early on so he has just been throwing bullpens and sides," Anthopoulos said. "We want to be careful with him just because he did have a setback early. It wasn't severe, but we just weren't going to take any chances.
"He had been built up to go two innings and then had some soreness in his elbow. So he may start a rehab assignment, but we're going to be 100 percent sure on him. He's probably still pretty far away."
In other injury news, left-hander J.A. Happ has continued to throw off a mound, but he won't be cleared for a rehab assignment until he feels completely healthy. Happ hasn't pitched since he was struck in the head by a line drive off the bat of Desmond Jennings on May 7.
The cruel twist of fate is that it's not the head injury which has continued to cause problems, but rather a sprained left knee he suffered on the same play.
"He's throwing batting practice but being able to get off the mound, field your position, do all of those things, our trainers have said you can't take that chance until there's no soreness," Anthopoulos said. "He'll get up in the morning, be a little sore, and once he starts to get going the soreness goes away. Until that pain is completely gone, he won't start an actual rehab assignment."