The reliever is headed to the disabled list.
"We're going to put him on the disabled list immediately, and he'll go to Florida to get further examination," manager John Farrell said after the game.
The Blue Jays haven't made a roster move yet to replace Perez, who will join a long list of Toronto pitchers on the disabled list, including Sergio Santos, Brandon Morrow, Dustin McGowan, Jesse Litsch, Drew Hutchison and Kyle Drabek.
Perez entered the series finale against the White Sox with a 3.07 ERA. After allowing four hits and two runs, his ERA jumped to 3.43, though the Blue Jays held on for the victory.
"Today was a much-needed win, a hard-fought win, and yet a costly one with Luis Perez going down," Farrell said.