Davis suffered the injury after an at-bat during the eighth inning of Sunday's 5-4, 10-inning victory over the Angels. The 30-year-old hit a grounder to shortstop and came up limping on his way to first base.
"I felt good going up to the box," Davis said. "I think a couple of steps after my swing I kind of felt a pop in my leg, and I guess the rest is history."
Manager John Farrell and head trainer George Poulis ran onto the field at the time of the incident. Davis was examined and eventually removed from the game to undergo further evaluation.
The club will run additional tests on Davis' left leg in the near future, but there is no immediate time frame for his return to action.
"I'm not sure, because this never happened in my career," Davis said when asked if he knew how long rehab would take. "This is a first for me.
"I think things happen for a reason. You take the good with the bad. I just don't consider everything like this bad. I'm going to look for the good out of it, and who knows what's around the corner for me."
Davis entered play Sunday hitting .238 with one home run and 29 RBIs in 94 games this season. He is currently ranked third in the American League with 34 stolen bases.
Toronto called up utility man Mike McCoy to take Davis' spot on the 25-man active roster. McCoy has appeared in 43 games with the Blue Jays this season and is batting .234 with one home run and five RBIs.