Michael Winchester, 52, was fatally wounded while walking between a crowded terminal and the airport employee parking area at Oklahoma City's Will Rogers World Airport.
The unidentified suspect was later found dead in a pick-up truck in a public parking garage overlooking the scene, after suffering an apparently self-inflicted gunshot wound.
Oklahoma City Police captain Paco Balderrama said the gunman apparently knew the victim's schedule and routine.
"This individual went there and waited for the employee to either be coming or going to take this opportunity," Balderrama said. He would not say conclusively that it was a "sniper-type" attack.
The 1pm shooting set off an alert at the airport, with police immediately closing the sprawling complex and asking passengers inside to seek cover.
Officers diverted incoming flights and refused to give already-loaded aircraft permission to leave.
There were concerns the gunman might have entered the terminal and mingled among passengers or employees.
"We have a heightened level of security all the time. These people have access to aircraft so we're very concerned about that," airport spokeswoman Karen Carney said.
"It is with great sorrow that Southwest Airlines confirms that a Southwest Employee who was injured during a shooting incident today at Will Rogers World Airport in Oklahoma City has died from injuries," the airline said in a statement.
It cancelled flights out of the city for the remainder of the day, even though the rest of the terminal planned to reopen.
Carney said about 300 people were held on aircraft away from the terminal after their planes landed.
Once police determined that a suspect found in a red pick-up truck on the second floor of a public parking garage was dead, officers gave an all-clear.
Victim Michael Winchester was a punter on the University of Oklahoma's 1985 NFL national championship team.
"Our hearts are truly heavy for the entire Winchester Family. Mike was a former Sooner student athlete as was his son James/daughter Carolyn," the school's athletic director, Joe Castiglione, tweeted on Tuesday afternoon.
He added: "daughter Becca was also a student athlete. Please keep this beautiful family in your prayers", in a later tweet.