Hamburg Police said on social media: “The LKA negotiating group and psychologists are on site.”
BBC Economics Editor Faisal Islam tweeted: “Rather unsurprisingly BA captain has just emerged to tell us the evening flight from Heathrow to Hamburg has just been cancelled with all of us on board…”
Police said no one appeared to be injured but the airport took the step of closing for takeoffs and landings.
A large number of officers from state and federal police were on site and in the vicinity of the vehicle, federal police spokesman Thomas Gerbert told German news agency dpa.
Bild reported that at about 8pm local time the gunman drove in front of Terminal 1 in an Audi without a number plate.
The driver had originally sped away but a few minutes later broke through a security barrier at the north gate and drove towards the planes.
Special forces were also sent to the airport.
This is a breaking story, more follows