The tourist boat was carrying 27 people, including 15 English tourists, off the coast of the city of Marsa Alam, according to Al-Ahram.
Twelve of the British tourists were rescued and the search for the remaining three is underway, according to Al-Ahram.
The state outlet didn’t mention how the fire started.
A spokesperson for the UK’s Foreign Office (FCDO) said in a statement Sunday that they are “in contact with local authorities” and are supporting British nationals involved.
The incident comes just days after beaches were closed in the Red Sea resort of Hurghada, after a Russian man was killed in a shark attack.