The 28-year-old Stroman, 5-9 with a 3.18 earned-run average, will make his first all-star game appearance.
He will be joined at the all-star break on July 8-9 by Blue Jays rookie third baseman Vladimir Guerrero Jr., who will compete in the home run derby.
In his latest outing on Saturday, Stroman left the game early after throwing two pitches in the fifth inning because of some discomfort in his non-throwing shoulder.
He was diagnosed with a left pectoral cramp, but he remarked after the game he didn’t expect to miss his next start.
Stroman began to feel tightness in his left shoulder as he warmed up for the inning.
"I thought it was something I could work out over the next few pitches," said Stroman, who could be moved before next month’s July 31 trade deadline. "I thought with my intensity level it would have kind of fixed itself. It was just there. I was just being cautious.
"I’m not worried. I’m a warrior, I’m a dog. I fully expect to be out there in five days."