The accident occurred in the city’s Hazirhat Monthona area of the Rangpur-Dinajpur Highway around 7am on Sunday, said Kotowali Police OC Mukhtarul Alam.
Two of the dead have been identified as Saju Mia, 35, and Chan Miah, 34.
The Hanif Enterprise Bus was headed from Dhaka to Thakurgaon when the driver lost control of the vehicle and struck an autorickshaw going in the opposite direction, OC Alam said, citing witnesses.
Saju and Chan died on the scene. Four people injured on the crash were on their way to Rangpur Medical College Hospital when one of them died.
One of the wounded is in critical condition, said RMCH Assistant Director Shafiqul Islam.
The bodies have been kept at the hospital morgue and the bus involved in the accident has been impounded, said OC Alam.