Local officials say 39 others were rescued after the vessel sank at around 10:00 local time. Unconfirmed reports suggested the vessel hit a reef and lost pressure.
Two married doctors are among those who have died and their daughters remain in hospital, authorities said. A Russian official said that two others who died were children, according to Tass, Russia's state-owned news agency.
This is the second incident involving a tourist vessel in the Red Sea in recent months. In November, a boat capsized near Marsa Allam, which left 11 people missing, presumed dead.
The Red Sea governor, Amr Hanafy, said passengers on the "Sindbad" were from Russia, India, Norway and Sweden. Five Egyptian crew members were also on board.
Mr Hanafy said the six who died were all Russian, but full details of the victims have not yet been released.
An investigation into the incident is ongoing but the Association of Tour Operators of Russia cited in a Telegram post unconfirmed reports that the submarine hit a reef and subsequently lost pressure while at a depth of 20 metres (65 feet).
The city of Hurghada is located to the south-east of Cairo - a tourist destination which is known both for its beaches and coral reefs.
Dr James Aldridge from Bristol took the same trip on the submarine in February 2025. He told the BBC: "The sub was well-maintained and was as shown in the promotional photos.
"Fresh paint, modern equipment and with attentive and professional English-speaking staff (including two divers to accompany you down)."
He explained passengers listened to a safety briefing, which had been recorded in multiple languages, and said that life jackets were not issued.
"We toured the reef for 40 minutes. For the first 20 I was facing the reef, the sub never strayed 'too close' and I never felt unsafe. For the return trip, I was facing the ocean," he added.
