Muhammad Javed, the 26-year-old chief of the military wing of Jamaatul Mujahideen, was arrested on Monday night along with four other members of the group in the port city of Chittagong.
Senior police official Babul Akter said Javed was killed while he was helping police recover more weapons in Chittagong.
Read: Bangladesh arrest suspected local militant chief
“The grenade exploded when the team was trying to recover it from a drain,” Akter said. Two policemen suffered minor wounds, he added.
Bangladesh has been convulsed by rising violence over the past year in which four online critics of religious militancy were hacked to death, a US citizen among them. Attacks on foreigners are rare in Bangladesh.
The South Asian nation is on alert after two foreigners were shot dead last week in attacks claimed by the Islamic State group, although police said there was no evidence the group was behind the attacks.
Jamaatul Mujahideen fighters have been sought since the group detonated nearly 500 bombs across Bangladesh on a single day in 2005. Later attacks on several courts killed 25 people and wounded hundreds.
Police said nine hand grenades, 120 rounds of ammunition, pistols, knives and a large quantity of bomb-making materials were seized in Monday's raid.
Read: Bangladesh arrests militant chief over blogger murders
Separately, police arrested a member of the student wing of the Jamaat-e-Islami party on Tuesday in connection with an attack on a Christian priest in northwest Bangladesh.
Three Muslim men tried to slit the priest's throat while he was preaching, police said.
Attacks on members of Bangladesh's small Christian community are rare.
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