Two of those missing are British, the BBC understands. Finland has confirmed one of their nationals is unaccounted for, while authorities say four Egyptians are also missing.
The boat with 44 people on board - including 13 crew - sent a distress signal at 05:30 (03:30 GMT), according to the governor of Red Sea province.
Authorities have not indicated the possible cause of the incident, but added accounts of people onboard mentioned a wave hit the boat and caused it to capsize. Weather forecasters had warned against marine activities for Sunday and Monday.
The Sea Story left port near Marsa Alam on Sunday for a five-day diving trip, according to officials.
Red Sea Governor Maj-Gen Amr Hanafi said the survivors were found in the Wadi el-Gemal area, south of Marsa Alam, and that they were receiving the necessary medical care.
He added the Egyptian Navy warship El Fateh and military aircraft were intensifying their efforts to locate the missing, with rescue teams working around the clock.
On Saturday, the Egyptian Meteorological Authority forecast turbulence on the Mediterranean and Red Seas due to the weather.
Wind speeds were between 37-43 mph (60-70 km/h), and wave heights were three to four metres (10-13ft) high, they said.
MNA/