About 600,000 refugees from Myanmar live in the huge camp in the city of Cox's Bazar in Bangladesh.
The fire broke out at 16.00 local time according to the daily newspaper Dhaka Tribune.
Due to strong winds, the fire is spreading rapidly among tents and sheds, local media reports.
Several units from the rescue service are on site at the refugee camp and are working to put out the fire.
According to information to Norwegian VG, it has burned in the camp before, but never to the same extent.
There are no reports of injuries in connection with the fire.
The article is updated.