Sunday afternoon's accident on the Dhaka-Sylhet Highway in Ashuganj Upazila left three others injured.
All the victims were passengers of the car, police said identifying one of the dead as Nuruzzaman, 30.
The injured have been admitted to Brahmanbarhia Sadar Hospital.
Khatihata highway police's Sergeant Abdun Nur said a sand-laden truck rammed into the Dhaka-bound private car killing three on the spot.
Nuruzzaman died after being taken to a local hospital, he said.