Play was halted for four minutes in the seventh inning while the fan received CPR and was carted off on a stretcher.
Ambulance sirens could be heard outside the stadium as the fan was carted off, still receiving CPR.
Following the game, Toronto Police Services confirmed the fan had died in a hospital after collapsing. The name of the fan was not released.
"Our thoughts and prayers go out to the family of the person who was taken out of here tonight," Blue Jays manager John Farrell said.
White Sox third baseman Kevin Youkilis was the first player to notice the commotion in the stands, and alerted umpire Mark Wegner to what was going on.
"I saw some medics jump out around the dugout and run over," Youkilis said. "Then I saw a doctor or whoever was going, just pushing on the chest over and over and over. I thought maybe they were reviving him and then the next thing you know, they kept going and going. I was like 'God, man. We've got to stop this thing.'"
Wegner approached second base ump and crew chief Mike Winters after Moises Sierra hit a foul ball down the right-field line, and the game was stopped to allow a cart to come onto the field and carry the fan off through the left field gate.
Blue Jays players left their dugout to watch as paramedics pumped the man's chest repeatedly.
White Sox pitcher Jesse Crain, who was on the mound at the time, was left shaken by the episode.
"I said a little prayer for him after everything started going again," Crain said. "You don't ever want to see that."
This was the second time this season a fan received CPR at a Blue Jays game; it also happened June 29.