Two bombs went off within the space of a few minutes in Netrokona, 360km north of the capital Dhaka.
Police said the wounded included three policemen.
Many of the victims were people on their way to work at offices, colleges and markets, witnesses said.
One police officer said: "We have reasons to believe that one among the dead was a suicide bomber, who arrived on the spot on a bicycle just moments before the blast," he added.
Police said they found another bomber among the wounded, with an unexploded bomb strapped to his body. He was taken to hospital unconscious, police added.
"Two of the dead, including a woman, have been identified, but identities of the rest are yet to be ascertained," one
police officer said.
No one has claimed responsibility for the attack but police blamed a group called Jameyatul Mujahidin which is seeking to impose strict religious law in the Muslim nation and has been held responsible for a string of blasts.
Sana Ullah Sheikh, additional superintendent of police said, "we believe it's the work of Jameyatul Mujahidin."
Police, judiciary and official
buildings have been targeted
Fifteen of the injured in the attack in a busy street were in critical condition, he said.
Nine of the injured were policemen who had been called to the site to defuse another bomb, Sheikh said.
A series of bomb attacks targeting the police, judiciary and official buildings began in August.
Including Thursday's blast, the attacks have claimed the lives of 23 victims including two judges. Four suicide bombers have died too.
Jameyatul Mujahidin leaflets calling for the institution of Islamic law in the country of 140 million people have been found at many of the blast sites.