"There is panic here," said an officer at the police control room in Kishoregonj town.
Administrative district chief Mohammad Azimuddin Sheikh said initial suspicion was that the explosion near a school was caused by a militant bomb.
One suspected attacker was also killed, said another Kishoregonj police officer, Anwar Hossain Khan.
Ramadan ended this week with the Eid al-Fitr festival across the Muslim world.
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