The shootings happened at the baggage claim area in Terminal 2, just before 1300 local time (1800 GMT), according to airport officials.
Hundreds of people were standing on the tarmac outside the terminal as dozens of police cars and ambulances rushed to the scene.
A witness told MSNBC that the gunman was a "slender man' who was wearing a Star Wars T-shirt.
The gunman, who appeared to be in his 20s, did not speak before or during the attack, John Schlicher said.
He added that his mother-in-law administered first aid to someone who had been shot in the head.