The blaze started in a market store at the Kutupalong camp, home to more than 600,000 Rohingya refugees, in the early hours and quickly spread to seven nearby shops.
Three young men aged between 13 and 22 asleep in one of the stores were killed, police and fire officials said.
On March 22, a devastating fire killed 15 Rohingya and left nearly 50,000 homeless.
Two other serious fires this year have also set alarm bells ringing over safety conditions in the camps where about one million of the Muslim refugees have been living since fleeing military clampdowns in neighbouring Myanmar in recent years.
Local fire chief Imdadul Hoque said the latest blaze would have been catastrophic had it not been quickly controlled as the market is close to tens of thousands of highly inflammable bamboo and tarpaulin shanties where most of the Rohingya live.
Hoque said five people were sleeping in a clothing shop when the fire broke out. "Two escaped but the other three were trapped in a bathroom in the shop."
Police said they believe an electrical short-circuit caused the fire.
They are still investigating the cause of the March 22 blaze which destroyed 10,000 shanties.
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