The 48-year-old man who died was a resident of Rome, while the injured man was 69, according to AFP.
Egyptian officials said the two tourists were transported to a hospital in Port Ghalib, around 30 miles north of Marsa Alam.
The swimming area in Marsa Alam will be closed and the incident is being investigated, authorities said.
In the past 10 years, there have been four confirmed fatalities due to shark attacks, according to data compiled by the independent Shark Research Institute.
The last to occur happened in June 2023 near Hurguda and involved a 24-year-old Russian man.