The wife of Farhad Mazhar, a well-known poet, writer and dissident, told police he telephoned early today to tell her he was being taken away by a man and feared he would be killed.
Shortly afterwards, she received a ransom demand for her husband.
"His wife sent a man to the (police) station who told us Mazhar called few hours later after he left and said that he was being taken away and would get killed," said duty officer Aleya Akhter.
Police said they were investigating but had not yet registered a case as the family had not formally reported him missing.
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CCTV footage of Mazhar's neighbourhood in the capital Dhaka showed him walking away with a man early in the morning.
The 69-year-old is a supporter of the country's main opposition Bangladesh Nationalist Party (BNP).
BNP officials have said tens of thousands of their activists and supporters have been arrested by the government since 2014, when the party boycotted a controversial general election over fears it would be rigged.
Kidnapping for ransom is relatively rare in Bangladesh, and rights activists urged the government to properly investigate Mazhar's disappearance to prove it was not involved.
"Such incidents happen repeatedly and the government's silence is deplorable," said Nur Khan Liton, a prominent rights activist.
Rights group Ain O Salish Kendra says 39 people have gone missing in Bangladesh so far this year including top political and business figures.
Mazhar had on Sunday taken part in a press conference to protest a spate of lynchings of Muslims in India, a key ally of the current regime in Bangladesh.