The bodies were found in one of the 20 shops that were gutted after the fire broke out at the market near Kutupalong refugee camp, fire brigade official Khisha Khoi Marma told dpa news agency.
The accident occurred near the sprawling Rohingya refugee camps in the district, nearly 325 km south-east of the capital Dhaka.
The men who died were aged between 20 and 25 and had worked at a clothing shop that was destroyed, Marma said.
They might have been sleeping inside the shop when the fire broke out, he added.
An electrical fault could have caused the blaze, according to Emdadul Haq, head of the local Fire Service and Civil Defence department.
An investigation has been launched to determine the cause of the fire, Haq said.
Last month, a huge fire destroyed four refugee camps, killing at least 15 people and leaving more than 45,000 others homeless, according to the UN Refugee Agency.
More than 1 million Rohingya Muslims have been living in 34 squalid camps built on more than 3,000 hectares of hilly land in Cox's Bazar since they fled persecution in Buddhist-majority Myanmar.
Nearly 750,000 of them crossed the border after Myanmar launched a military crackdown on the ethnic group in 2017.
Dhaka, April 2
At least three Rohingya men died on Friday after a blaze gutted shops at a makeshift market near a refugee camp in Bangladesh's Coxs Bazar district, firefighters said.
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