Marks showing that the coach had skidded on a tight bend were found on the road.
Mena, Egypt’s news agency, said that the accident occurred at 6am [0300GMT].
Wounded passengers were taken to hospitals near Sharm el-Sheikh.
Two Russians and a Ukrainian have been reported to be among the dead. A Canadian woman had to have a hand amputated, a hospital official said.
Egyptian roads are considered highly dangerous with scores of people dying in crashes on them annually. Regulations are not fully enforced and vehicles badly cared for.
About 6,000 people die and 30,000 are injured in road accidents in Egypt annually.
Two coaches hit each other head on in March killing 23 people.
An accident south of Cairo involving multiple vehicles killed 29 people in February.