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.
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.