The six, who include poets, bloggers and a journalist, all live in the southern city of Barisal and went to police after their photographs appeared late yesterday on a new Facebook page registered under the name Ansar-BD.
"There are three anti-Islamic poets and three organisers of bloggers. They are the enemy of Islam. We should do whatever it takes," read the post.
Police said they did not know who was behind the threat but were taking it seriously, and the country's elite security force was investigating.
The apparent hit-list was published less than a week after blogger Niloy Chakrabarti was hacked to death at his home in the capital Dhaka by an unknown attacker.
Also Read
He was the fourth atheist blogger to have been killed since February when Bangladeshi-born US citizen Avijit Roy, a writer and moderator of a blog site, was hacked to death in Dhaka.
The Bangladesh branch of Al-Qaeda in the Indian Subcontinent, Ansar al-Islam, claimed the murder of Chakrabarti and warned of more to come, according to monitoring group SITE.
Journalist Nazrul Biswas was among those threatened. He said he was not against Islam and refused to be intimidated.
"We raise our voice for a secular society and against militancy and fundamentalism. No threat can stop us," Biswas told AFP.
The list was published as New York-based rights group Human Rights Watch urged Bangladesh authorities to unequivocally declare their commitment to free speech instead of proposing self-censorship.
"It's shocking that Bangladesh authorities not only failed to protect the bloggers despite complaints to the police about threats against them, but instead are proposing self-censorship," said Brad Adams, Asia director at HRW.