General manager Alex Anthopoulos said the 23-year-old right-hander will seek a second opinion from Dr. James Andrews, and surgery is likely.
Anthopoulos said Stroman was participating in bunting practice when he was called off by third baseman Josh Donaldson. Stroman planted his feet to stop, then felt a pop in his knee.
An MRI confirmed the tear.
"Beyond devastated," Stroman tweeted. "Not being able to compete with my brothers each and every day is extremely disappointing. Still can't believe it."
It was the second significant training camp injury for the Jays. Canadian outfielder Michael Saunders tore the meniscus in his knee in a freak accident when he stepped into a sprinkler head indentation while shagging fly balls.
The prognosis was better than expected for Saunders after having 60 per cent of his meniscus removed. He could be ready for Opening Day.
Stroman is expected to take much longer to heal.
"It's one of those things," Anthopoulos said. "(It was) not expected and bad luck I guess."
His injury leaves a void in the Jays rotation, which had looked to be R.A. Dickey, Mark Buehrle, Stroman, Drew Hutchison and a pitcher still to be determined.
And it may push the Jays into using Aaron Sanchez as a starter rather than closer. Other starting options are Daniel Norris and Marco Estrada, who were battling for the fifth spot in the rotation.
"No doubt to lose a guy like Stroman is a significant loss for us," Anthopoulos said. "But you move forward and it's going to be an opportunity for some of the other guys that are here."
Former Cy Young Award winner Johan Santana is a longshot to be in the mix. He is trying a comeback with the Jays, but is still some time away from seeing if he still has the goods.
Stroman, a 2012 first-round pick, appeared in 26 games for the Blue Jays last season. He went 11-6 with a 3.65 earned-run average and 111 strikeouts in 130 2/3 innings.
The native of Medford, N.Y., had been all smiles in camp this year, more at ease with in the clubhouse after a year in the major leagues.
"Last year being a young guy coming into your first spring training, you can't really be yourself,'' he said recently. "And I'm pretty flashy, I talk a lot. This year I'm able to do that.''
And with six pitches in his repertoire including a newly minted sinker, Stroman has plenty of weapons on the mound.
He was off to a good start this spring. Stroman had not given up an earned run in 4 1/3 innings over two pre-season appearances.
"We all know the energy he brings and how badly he wants to win and be a part of this team," Anthopoulos said. "It's just one of those things. He's probably the best athlete on the team and is in as good of shape as anybody you're going to have. He's the last guy you would expect for that to happen.
"Again, it's just a freak thing. But we move forward."
The Jays were looking for big things from Stroman in 2015.
"He's that good. And he's that confident." manager John Gibbons said last week.
A muscular five foot eight and 180 pounds, the outgoing Stroman is very comfortable in his own skin.
"I feel a lot different, I feel much more relaxed,'' he said last week. "I'm focused, I know what I have to do rather than doing everything in my power to go out there and trying to make the team, doing more than I had to.
"I'm relaxed, I'm motivated, I'm ready to go.''
The Blue Jays dropped a 5-3 decision to Minnesota in pre-season action Tuesday. Stroman was not available after the game but posted another tweet later in the afternoon.
"Appreciate the love," he tweeted. "Don't be upset though. I promise to be back even stronger with a bigger smile. Faith and confidence define me!"
With files from The Associated Press.