The mishap caused disruption of rail traffic, the police said.
The incident took place in Nokha police station area of the district in the early hours when dense fog had engulfed the area, SHO Shashi Bhushan Prasad said.
The Bolero car was mangled under impact of the collision though the train was moving at a very slow speed, Prasad said.
Locals rushed to the spot upon hearing the scrunch and took out the three occupants - identified as driver Mohammed Wasim and passenger Deepak Kumar and Poonam Devi.
The badly damaged Bolero car was removed from the railway tracks and movement of trains on the Ara-Sasaram section was resumed after about a couple of hours, the SHO added.