The governor of the Red Sea region Amr Hanafy said rescuers saved 28 people from the vessel south of the coastal town of Marsa Alam and some were airlifted to receive medical treatment.
Hanafy said 31 tourists from various countries were on board along with 14 crew.
The governorate received a report shortly before dawn on Monday of a distress call made from the yacht, which had left Marsa Alam for a five-day journey.
It was not immediately clear what caused the four-desk, wooden-hulled motor yacht to sink. Â
But the Egyptian Meteorological Authority on Saturday warned about turbulence and high waves on the Red Sea and advised against maritime activity for Sunday and Monday.
A person answering the phone at the company that operates the yacht, Dive Pro Liveaboard in Hurghada, Egypt, told the Associated Press they have "no information" and hung up.
According to their website, the Sea Story was built in 2022 and can hold 36 passengers.
The Egyptian military was co-ordinating rescue operations with the governorate.
Many tourist companies have stopped or limited travelling on the Red Sea due to the dangers from conflicts in the region.
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