Several agreements between Qatar and Bangladesh are to be signed following bilateral talks
The car met the accident near Salehpur Bridge after crossing Aminbazar on Sunday night, according to police and Fire Service and Civil Defence.
An official at fire service control room said divers had launched a rescue operation.
Aminbazar Police Camp Sub-Inspector Jamal Hossain said no-one could confirm whether there was any passenger besides the driver on the car.
Jasim uddin Joy, a witness, said he saw the yellow car fall into the river when a bus was overtaking it.
Joy said he called national emergency helpline 999 immediately after the incident.