The 21-year-old rookie left Friday night's 3-0 win over the Philadelphia Phillies after just nine pitches.
The Jays recalled right-hander Robert Coello from Triple-A Las Vegas.
"I think everything right now points to avoiding surgery," Blue Jays manager John Farrell said before Saturday's game against the Phillies. "Time will be needed for it to heal, to allow that sprain to become more secure. The only thing we don't know is how long that will take."
Hutchison, who is 5-3 with a 4.60 ERA in 11 starts, is the third Toronto starting pitcher to go down in five days.
"This is the first of any arm problems that I've had," he said. "It's not ideal."
Kyle Drabek has a torn ligament in his elbow that may require surgery. Drabek left in the fifth inning of Toronto's 6-2 loss to Washington on Wednesday.
Brandon Morrow left Monday's 6-3 loss to the Nationals after just nine pitches with a strained oblique muscle in his left side. He's also on the 15-day DL.
"After seeing everything that's gone on, it's tough," Hutchison said. "The team's in a tough spot and you want to go out and help anyway you can and you come up with it yourself. But it is what it is. I'm going to try to get back and help the team."
Added Farrell: "Unfortunately, pitching is a game of attrition and we're seeing a lot of (injuries) right now."
The 27-year-old Coello spent time with the Blue Jays this month, holding the Boston Red Sox to three hits and no runs in two innings June 1.