The airport closed for all takeoffs and landings shortly after the incident at around 8pm Saturday local time.
The car with the 35-year-old man and 4-year-old child was parked under a plane, a police spokesperson said, and officers were at the scene with a large presence late on Saturday.
Police said it was likely a custody dispute. The mother told police the father had been in contact with her about the act.
Police would not confirm their earlier statements that the man was armed and had fired shots.
A spokesperson for the airport said 27 flights had been affected.