Stroman, a right-hander with Double-A New Hampshire, tested positive for Methylhexaneamine, a banned stimulant. Stroman, who played college ball at Duke, received a US$1.8 million bonus when he signed with Toronto last month.
In a statement, the Blue Jays said Stroman tested positive while playing for class-A Vancouver.
"Despite taking precautions to avoid violating the minor league testing program, I unknowingly ingested a banned stimulant that was in an over-the-counter supplement," Stroman said in the statement. "Nonetheless, I accept full responsibility and I want to apologize to the Toronto Blue Jays organization, my family, my teammates, and the Blue Jays fans everywhere. I look forward to putting this behind me and rejoining my teammates."
Two more minor leaguers received 50-game penalties on Tuesday.
First baseman Mark Donato, who plays for Kansas City's rookie-league team in Arizona, tested positive for an amphetamine. Tampa Bay outfielder Joshua Sale, who was at Class-A Bowling Green, was penalized for testing positive for methamphetamine and an amphetamine.
The 21-year-old Sale was drafted in the first round (17th overall) in 2010. He was hitting .264 with 10 homers, 44 RBIs and a .391 on-base percentage in 74 Midwest League games this season.
Each of the suspensions is effective immediately.
Stroman, 21, was 3-0 with a 3.26 ERA in 15 combined relief appearances with Vancouver and New Hampshire. He had 23 strikeouts and nine walks in 19 1-3 innings.
"This suspension is unfortunate and we are disappointed by this development. The Toronto Blue Jays however fully endorse Major League Baseball's drug testing policy and support the discipline taken today," general manager Alex Anthopoulos said in the statement.