Sportsnets' Shi Davidi reports that the injury occurred during pitchers fielding practice on Tuesday.
Stroman was entering his second season in Toronto after being selected in the first round of the 2012 draft.
Over 130 2/3 innings last season, the 23-year-old recorded a 3.65 ERA with 111 strikeouts and 28 walks.
Stroman struck out four batters and allowed zero earned runs over 4 1/3 innings this spring.
Last season, the Blue Jays went 83-79 and finished in third place in the American League East.
Beyond devastated. Not being able to compete with my brothers each and every day is extremely disappointing. Still can't believe it.— Marcus Stroman (@MStrooo6) March 10, 2015
- Chris Johnson