Video from a television station helicopter showed what appeared to be a pool of blood near the bottom of a ramp leading from the airport's departure area. Two ambulances and a firetruck stood by.
Oklahoma City Police Capt. Paco Balderrama said the victim had died. The agency said on its Twitter feed that the airport remained closed.
"We can confirm that victim from shooting at WRWA (Will Rogers World Airport) is deceased. Airport still on lockdown as investigation is ongoing," the department tweeted.
Balderrama initially said police had received reports of a possible second victim, but no one had been located by late afternoon. Police were still sweeping the terminal building on the city's southwest side. No other details of the shooting were immediately available.
The airport suspended operations and maps posted at the FlightAware website showed that one flight was diverted to the Wiley Post Airport in the northwestern part of the city while two commercial flights from Chicago's O'Hare Airport were directed to Tulsa, about 100 miles away. A jet carrying federal inmates was allowed to land. Oklahoma City is a major transfer point for federal inmates.
"There are going to be some delays for flights until we have further information," airport spokeswoman Karen Carney said, while referring other questions to police.
All streets were blocked off surrounding the airport and everyone should avoid the area, Balderrama said. Some people were allowed to leave the grounds after police checked their vehicles.
Carney said Southwest, American, Delta, United and Alaska airlines each have terminals at the airport, which handles about 7,000 to 8,000 passengers daily.
Carney said that police believe the shooting was an isolated incident, but that precautionary measures were still appropriate.
Associated Press reporters Ken A. Miller and Tim Talley contributed to this report.
Copyright 2016 The Associated Press. All rights reserved. This material may not be published, broadcast, rewritten or redistributed.