No casualties have been reported. But the blaze razed 2,000 shelters after spreading quickly through gas cylinders in kitchens, officials said.
Police are investigating if the fire was an act of sabotage. One man has been detained, local media reported.
The camp in the south-east is believed to be the world's largest refugee camp.
Most of its residents, Rohingya refugees, had fled persecution in neighbouring Myanmar.
On Monday, hundreds had returned to the area, known as Cox's Bazar, to see what they could salvage from the ruins.
The blaze had started at about 14:45 local time Sunday (08: 45 GMT) and quickly tore through the bamboo-and-tarpaulin shelters, an official said.
"Some 2,000 shelters have been burnt, leaving about 12,000 forcibly displaced Myanmar nationals shelterless," Mijanur Rahman, Bangladesh's refugee commissioner, told AFP news agency.
The blaze was brought under control within three hours but at least 35 mosques and 21 learning centres for the refugees were also destroyed, he added.
Photos are now emerging that show the extent of the devastation.
Many of those who lived there can be seen picking through the charred area, where only metal struts and singed corrugated roofing remains.
Hrusikesh Harichandan, from the International Federation of Red Cross and Red Crescent Societies, told the BBC there had been "massive damage" to the camp.
He said basic services such as water centres and testing facilities had also been affected.
"My shelter was gutted. [My shop] was also burnt," Mamun Johar, a 30-year-old Rohingya man, told AFP.
"The fire took everything from me, everything."
Thick black clouds were seen rising above Camp 11, one of many in the border district where more than a million Rohingya refugees live.
The camps, overcrowded and squalid, are vulnerable to fires.
Between January 2021 and December 2022, there were 222 fire incidents in the Rohingya camps including 60 cases of arson, according to a Bangladesh defence ministry report released last month.
In March 2021, at least 15 people were killed and some 50,000 were displaced after a huge fire tore through a camp in the settlement.
The refugee camp houses people who fled from Myanmar following a military crackdown against the Rohingya ethnic minority.
The Rohingya are Muslims in largely Buddhist Myanmar, where they have faced persecution for generations.
The latest exodus of Rohingya escaping to Bangladesh began in August 2017, after Myanmar's military brutally retaliated when a Rohingya insurgent group launched attacks on several police posts.
-- Courtesy of BBC News