He then shot himself in the car park in front of team officials.
The club confirmed the incident in a statement, adding: "We are co-operating with authorities in their investigation."
Kansas City police spokesman Darin Snapp told AP news agency that authorities were told early on Saturday that a woman had been shot five miles away from the Arrowhead complex.
The victim was later identified as Belcher's girlfriend.
Police were then called to the training facility, where they saw the player in a car holding a handgun to his head. He thanked the Chiefs' general manager Scott Pioli and coach Romeo Crennel for all they had done for him before shooting himself.