The minibus and the coach, which had come from the capital Cairo and was heading for the Red Sea tourist resort of Sharm el-Sheikh, collided while speeding in poor visibility due to fog around dawn, officials added.
The crash took place close to El-Tor in southern Sinai, some 300 kilometres (185 miles) southeast of Cairo.
The casualties were taken to a hospital in El-Tor.
Travel accidents are frequent in Egypt, where many roads are badly maintained and traffic rules often neglected.
About 7,000 people were killed on the country's roads in 2020, according to official figures.
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