The suspect was found in a truck in a parking garage, said Capt. Paco Balderrama of the Oklahoma City Police Department. The suspect, who was shot in the head, has not been positively identified.
Balderrama said the shooting was not random.
"It's too early in the investigation to figure out the exact motive, although the crime does appear to be premeditated," he said.
The captain said it appeared the suspect waited in his truck for the victim, a Southwest Airlines employee named Michael Winchester, to either arrive for or leave work.
The airline said, "The Southwest Airlines family is deeply saddened by the passing of our Southwest family member, and we extend our heartfelt sympathies and support to his family and Southwest co-workers at this time."
Officials didn't disclose what role Winchester, 52, held at Southwest. A since-deleted LinkedIn page described Winchester, a former member of the popular Oklahoma Sooners football team, as a ramp supervisor.
The airport was closed to commercial traffic for hours, though one government plane landed.
As they swept the terminal looking for the suspect, police advised anyone inside the facility to "shelter in place."
About 7 p.m. CT, the airport tweeted it was resuming operations.
Authorities went deck by deck in a parking garage, Balderrama said. The suspect's red pickup was found on the second level.
It is unclear if the shooter and victim knew each other, but "we have some basic information who the suspect might be," Balderrama said.
Shots were fired near a parking lot, he said.
The Winchester name is well-known to fans of the Oklahoma Sooners sports programs. Winchester and his son played football for the team. Mike Winchester was a punter in the mid-1980s and was a member of the 1985 national championship team.
According to the Sooners website, Mike Winchester was married and had three daughters and one son.
His son, James Winchester
, is a special teams player for the Kansas City Chiefs.
His sisters, Carolyn (basketball) and Becca (rowing), also played sports for the university.
"Please keep this beautiful family in your prayers," Sooners athletics director Joe Castiglione tweeted.
Five airlines fly out of Will Rogers to 21 destinations. The airport sees 150 commercial flights a day and more than 3.6 million passengers each year, the city's website says. At least 25 flights were canceled Tuesday, Will Rogers World Airport spokesperson Karen Carney said.
was waiting for his flight to Dallas when the airport went on lockdown. He told CNN that most people were calm. "There is that air of wanting to get going, " he said. "Most of us will miss our connections to wherever we are heading."
Southwest Airlines said it was canceling the remainder of its flights scheduled to depart Tuesday.