Police accuse Abdul Haque, a former teacher at an Islamic seminary, of threatening noted academics and writers in the name of the Islamic State (IS) group and local banned outfit Ansarullah Bangla Team (ABT).
Bangladesh teachers, students rally against latest killing
"He sent death threats via telephone and text messages using a fake IS identity," police spokesperson Monirul Islam said, adding that prominent secular intellectual Anisuzzaman, historian Muntasir Mamun and writer Mohammed Zafar Iqbal were among the targets.
Tensions are running high in Bangladesh after a series of killings of secular bloggers and a publisher as well as the murders of two foreigners.
Secular Bangladesh publisher dies in separate attack
Secular writers, academics and bloggers have received death threats in the wake of the killings, while some have fled overseas fearing for their lives.
Police have stepped up a search for those behind the threats as well as security of those targeted after a hitlist was published on the Internet of 153 names.
Tuesday night's arrest came as police announced a Bangladeshi man has also been detained for spreading IS propaganda on the Internet.
The government says the jihadist group has no presence in Bangladesh and instead accuses the opposition of trying to destabilise the country.
The country of 160 million mainly moderate Muslims has been known for its religious tolerance.
But Bangladesh has been plagued by unrest in the last three years, and experts have warned that a long-running political crisis has radicalised opponents of the government.
Security was stepped up across the country after two top opposition leaders were hanged on Sunday following their conviction for war crimes committed during the 1971 independence conflict against Pakistan.
Authorities fear violent protests by supporters of the opposition leaders.
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