Gibbons instead went to right-hander Drew Storen in the ninth inning vs. the Dodgers. Storen didn't allow a run, but he loaded the bases before getting Corey Seager to fly out and end the game.
"I pitched maybe too often, and maybe I pulled something," said Osuna, who has a 2.08 ERA in 13 innings this season. "I don't know exactly what happened. That's the movement when I throw to home plate ... I didn't feel it during the game, I just felt it after the game."
Osuna is expected to be ready for Saturday afternoon's game against the Dodgers. He has converted all 12 of his save opportunities this season, but his last chance came back on April 24.
"I was ready today, so tomorrow I should be fine," Osuna said through an interpreter.
Gregor Chisholm has covered the Blue Jays for MLB.com since 2011. Follow him on Twitter @gregorMLB and Facebook, and listen to his podcast. This story was not subject to the approval of Major League Baseball or its clubs.