The victim's identity has not yet been released; police said he was not carrying identification, nor was he dressed as an airport worker.
They do not suspect any suspicious activity.
Pictures of the aircraft, obtained by CBS, show a massive dent in one of the aircraft's engines.
"Southwest flight #1392 arrived safely this evening at Austin-Bergstrom International Airport (AUS) after being cleared to land on runway 17R," the company said in a statement.
"The Southwest aircraft maneuvered to avoid an individual who became visible on runway 17R shortly after touchdown. The aircraft quickly came to a safe stop, and the pilots reported the event to local air traffic controllers."