The deceased identified as Abdul Barek, 40, was the son of Abdul Goni of Karpashdanga village in the upazila.
Sukumar Biswas, officer-in-charge of Damurhuda Police Station, said police arrested Barek from Muktarpur village around 2:00am.
When police along with Barek was heading towards the police station, his associates opened fire on the law enforcers, forcing them to fire back in 'self-defence', the OC said.
At one stage, he said, Barek was caught in the line of fire and suffered bullet wounds.
Later, he was taken to Sadar Hospital where doctors declared him dead.
Four policemen were also injured in the incident, the OC added.
One pipe-gun, two bullets, two sharp weapons and phensidyls, kept in a sack, were recovered from the spot.
Barek was wanted in 15 criminal cases, according to the police record.