Two hours after his arrest, the 37-year-old man was found to have more than three times the legal limit of alcohol in his body.
His plane, part of the Sunwing budget airline, later left Calgary for Cancun, Mexico, with a different pilot. There were more than 100 people on board.
The incident happened at 07:00 local time (14:00 GMT) on Saturday.
Airline staff noticed the pilot behaving strangely, and then he passed out. They alerted the authorities and the man was escorted from the cockpit.