The Sea Story was carrying 30 tourists from several countries and 14 crew on a diving trip when it sent a distress signal at 5.30am local time (0330 GMT), according to Egypt's Red Sea governorate.
It was not immediately clear what caused the four-deck, wooden-hulled motor yacht to sink. There are unconfirmed reports that it was hit by a wave in high winds.
So far, 28 people have been rescued, leaving 16 missing including two from the UK, according to the BBC. The UK Foreign Office confirmed it was providing consular support to a number of British nationals and their families after the incident.
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