It is not yet known what caused the blaze. One eyewitness told the BBC that he believes an electrical fire was the cause.
A woman was taken away in a wheelchair, but it is not clear if that was connected to the fire.
Thousands of people are attending the UN climate talks, including members of delegations from around the world.
Nearly 200 countries are trying to agree on how to make progress in tackling climate change.
A member of the UK delegation said they were returning to their accommodation and that the fire had disrupted negotiations.
The BBC has asked the UN, who runs the summit, for more information about the cause of the fire and any impacts.
