The accident happened at around 4:50 am local time (0350 GMT) at a level crossing north of Neustadt am Rubenberg near the A6 autobahn, the Neue Presse reported.
A police spokeswoman said a regional train plowed into the car "at full speed" after the vehicle had driven onto the rail track.
She said the barrier was down at the time of the accident but that it didn't span the entire road.
According to police, the dead were the three young occupants of the car — the 22-year-old driver and women of a similar age.
Only one of the 42 passengers and rail workers on board the train was slightly injured.
A large contingent of emergency services personnel was at the scene.
Deutsche Bahn (DB) said the rail line between Hannover and Nienburg (Weser) would remain closed until lunchtime.
DB said all high-speed ICE trains between Oldenburg and Hannover have been canceled and other services would be affected.
The national rail operator said intercity trains Hannover and Emden were being diverted in both directions and delays could be expected.