In a statement on Thursday, the health ministry said the injured were taken to nearby hospitals for treatment and were being closely monitored.
The submarine was carrying 50 people, including five Egyptian crew members and 45 foreign tourists from Russia, India, Norway, and Sweden.
The six fatalities were identified as Russian nationals.
Earlier reports suggested that nine people had been injured in the incident.
The vessel was operated by Sindbad Submarines, a company that has provided underwater excursions in the Hurghada region for several years.
Short link: