Cleveland police Capt. Scott Felts says that at about 9 a.m., officials were called to a hangar at the airport regarding a shooting and found a 29-year-old man dead, lying face down.
Investigators determined that an ex-employee, identified as 20-year-old Marco Jacquez, arrived at the airport and approached the victim with a shotgun.
Jacquez allegedly demanded that the victim get into his car, but the man refused, causing the suspect to shoot the man several times.
Officials said the shooter fled the area in a 2016 silver four-door Nissan but was taken into custody and questioned by the Colorado County Sheriff's Office and Eagle Lake Police at 12:13 p.m., more than 100 miles away.
Officials said that the suspect was reportedly an ex-employee of a company based inside the airport and had recently returned to the Cleveland area for unknown reasons.
The victim's workplace inside the airport was not immediately clear.
Investigators are talking to witnesses to determine the cause of the shooting.
Jacquez is waiting for extradition to the Cleveland Police Department, officials said.