The accident occurred in Joypurhat railway station and the four victims died on the spot.
Some people were travelling to Dinajpur's Parbatipur on the train's roof, Station Master Nurul Islam said.
The victims fell when the train driver abruptly slowed down the train after realising that several compartments have been detached by miscreants, bdnews24.Com reported.
Those injured in the accident have been admitted to a nearby hospital.