A video of the 13-year-old's murder has gone viral on social media.
The killers accused the boy of trying to steal a bicycle rickshaw van in the north-eastern city of Sylhet.
Three people have been detained, including the main suspect who fled to Saudi Arabia after the attack.
Suspected thieves are often attacked by mobs in Bangladesh.
But the BBC's South Asia editor, Joanna Jolly, says that the brutality of the assault has caused widespread outrage and led to police forming a special squad to investigate the killing.
One of the attackers filmed the assault on Samiul Alam Rajon on Wednesday on his mobile phone, while the others tied the boy to a pole and hit him repeatedly with a metal rod.
He screamed for help, the Daily Star reported, and cried for water as he begged for his life.
The men can be heard laughing and jeering at him as they told him that they would post the video on Facebook.
After the boy was killed, the attackers took his body to a secluded dump, the paper reported, about 600ft (180m) away from the torture spot.
But they were spotted by some locals who chased them. Three of the group escaped, but one man was caught and handed over to the police. Another was later detained, while the main suspect was arrested in Saudi Arabia.
"It's a sad and unfortunate incident," Bangladesh's Home Minister Asaduzzaman Khan Kamal was quoted by bdnews.24 as saying. "One [man] has been remanded and another has been arrested. The rest will be arrested soon. None will be spared."
An autopsy report said that Samiul - who helped his family to sell vegetables - died of a brain haemorrhage after sustaining head injuries. More than 60 injury marks were found on his body. A Twitter page in his honour has been set up.

Alun Davies, who has responsibility for broadcasting, warned Wales had a "weakening" media and a lack of accountability was partly responsible.
But he stopped short of calling for devolved powers over the sector, during a media conference speech in Cardiff.
"I worry, and I am concerned, that Wales has a weak, indigenous media that is weakening," he said.
"And I am concerned that we don't always have the structures to enable us to have a conversation, apart from informally.
"The formal structures of accountability, formal structures of regulation and the formal structures to actually deliver policy.
"I think that is something which we do need to recognise, and is something that we need to debate and discuss.
"Not simply within government, or within the National Assembly, but within and throughout our society."
Mr Davies called for the assembly to have a greater role in holding media companies to account.
"I make no case for the devolution of responsibility for broadcasting to Wales or to the Welsh Government," he added.
"However, I do make the case for the accountability for broadcasting to be shared across the institutions of the United Kingdom."
Media bosses do give occasional evidence to assembly committees examining the media in Wales, but there is no formal arrangement that requires them to appear or submit evidence.
Since the renewal of the BBC's charter, the Welsh Government has been given a stronger role in appointing the Wales representative to the BBC board.
It used its veto to oppose the appointment of the UK government's choice for the position, Dr Carol Bell, earlier this year.
Dr Ruth McElroy, a media lecturer at the University of South Wales, said Wales' traditional media had weakened as the industry adapted to changing audience habits.
She told BBC Wales: "We have seen a great deal of closures of local newspapers. That's been a long-standing theme, and it's been greater in Wales than in the rest of the UK.
"I think what we have to do is be realistic that we are now in a digital age, and that modes of news delivery might be different in the future."
She added ministers should be more prepared to intervene to support media in Wales.
"There definitely is a place for government intervention. I think that sometimes, in the UK, we have been hostile to that, almost ideologically.
"In other parts of the world they are not, and they are reaping the benefits as a result."
Thousands of people in Bangladesh are demanding justice for a teenage boy who was beaten to death by a group of men who filmed themselves laughing and jeering as they carried out the attack.
[NEXT_CONCEPT]
Media companies should be more accountable to the National Assembly, a Welsh Government minister has said.