Police said the aircraft was on a training flight and took off from the airport at 12.45pm. Three minutes later, it crashed.
The two men in the aircraft died on impact and a series of explosions followed, the Weser Kurier reported.
The aircraft is believed to be a Saab Safir.
Videos from the scene show plumes of smoke from the crash site spreading across the area.
According to the Weser Kurier, around 100 firefighters and ten fire engines were at the scene on Friday afternoon.