They say that the government has ordered the three-part show off air because it could frighten children.
The hangman, who has hanged nine people in his 21 years in prison, has requested anonymity.
But he told the BBC that the programmes on the private channel, Banglavision, were mainly about his lifestyle.
The prison authorities wrote to Banglavision requesting them not to broadcast the programme, which “might affect the tenderness of the children and the mentality of the mass people of the country”.
Trained in jail
So far only one part of the series has been broadcast.
The letter wrtten to the TV station from the prison authorities said that it was in the public interest for the programmes not to be broadcast.
Programmes in Bengali on Banglavision are broadcast in many countries in Europe, the Middle East and the US.
“The motive of our programme was not a campaign against capital punishment or in favour of capital punishment,” said Banglavision Head of News Mostofa Feroz.
“It was just an offbeat story about the lifestyle of a hangman inside the jail. I do not understand how it breaches the jail code.
“A released man cannot be stopped from talking to the media – it is against the freedom of media and his freedom of rights,” he said.
The hangman started working as an executioner seven years ago and was trained for the job while serving a 30-year murder sentence – passed down when he was aged only 16 – for murder.
He was released early in August after getting 18 months’ time off for working as a hangman.
Bangladesh has executed 411 people since the country gained independence in 1971. All hangmen are prisoners or former convicts who have trained in jail for the job.
The unnamed hangman told the BBC that he carried out the hangings to reduce his time in jail.
“Although I did not like to hang anyone in the gallows, I did it to decrease the span of my jail term. For each hanging, I got two months’ exemption from my 30-year jail term,” he said.
The hangman said that his most memorable hangings were those of the killers of the country’s first president, Sheikh Mujibur Rahman – BBC