The deceased was identified as Anwar Hossain Yusuf, 45,son of Abu Taher alias Waliullah of Begumganj upazila.
He was a member of an inter-district robber gang and wanted in 12 criminal cases , said police.
Tipped off, a team of police conducted a drive at Jamidarhat in Begumganj uapzila on Monday night and arrested Yusuf around 9:30 pm, said assistant superintendent of Noakhali police, Alamgir Hossain.
Later, police along with Yusuf conducted another drive to recover arms around 2:45 am in Bircourt area of Senbagh upazila.
Sensing presence of the law enforcers, the associates of Yusuf opened fire on police, forcing them to fire back in self-defense.
Yusuf was caught in the line of fire and sustained bullet injuries.
Later, he was taken to Noakhali General Hospital where the doctors declared him dead.
Three policemen were injured in the incident.
One pistol, three bullets, four cartridges, seven shells of bullets, three sharp weapons and a gas lighter were recovered from the spot.