Stroman will appeal the suspension and be allowed to play until the process has played out.
The pitch came in the bottom of the sixth inning of Monday's game in Baltimore, which the Orioles won 5-2. Joseph was not hit, but the ball sailed behind him.
Baltimore manager Buck Showalter called Stroman's pitch "borderline professionally embarrassing" after the game, adding that it pushed the Orioles' "hot button" and wasn't called for.
"If you don't have the command to throw the ball where you're supposed to, to deliver a message, then you shouldn't be throwing at all there," said Showalter.
Stroman addressed the suspension on Wednesday and said he would never intentionally throw at a batter.
"It's in the appeal process now. I would never intentionally throw at anyone. I respect the game, I respect the players too much to ever do anything like that. Family, friends, teammates know the type of individual I am," he said.
The Orioles and Blue Jays wrap up a three-game series on Wednesday night and have one more scheduled series at the end of the season. Toronto is five games out of a wild-card spot in the American League, while Baltimore clinched the AL East for the first time since 1997 on Tuesday night.
- Molly Geary