The airport closed for all takeoffs and landings shortly after the incident at around 8 p.m. local time, Reuters reports.
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.
The cause for the actions of the man who broke into the Hamburg airport and had the four-year-old in the car could be the dispute over child custody, the DPA news agency said, citing a local police spokesman, TASS reported.
The man is presumably 35 years old. He parked his Audi car on the runway near a Turkish Airlines passenger jet. Law enforcement officials cordoned off the car and the first contact was established with the man. Talks with him continue. The traffic in the airport was halted completely.
MNA/PR