The incident took place in the Dhaur Bridge area of Ashulia at 11 pm on Saturday, said police.
The person has been identified as 36-year-old Bhola Das. He was a gold trader.
Three people, including Das, were travelling to Savar’s Tayebpur from Uttara at night, said Abdullahil Kafi, additional superintendent of Savar police.
The driver lost control of the vehicle after reaching the Maragang area. Das was trapped inside the car while others were able to escape.
Police and fire service personnel were able to pull Das’ body from the river after a half hour of rescue efforts.