It was travelling from Cairo when it turned over and was hit by the truck on a road in the southern province of Assiut, 199 miles (320km) south of the capital, said Assiut governor Essam Saad, SkyNews reported.
Both vehicles caught fire and photos show rescuers searching the burned-out bus for survivors.
Three others were injured and taken to hospital and 25 ambulances were sent to the scene on the Red Sea road, said a statement on the Assiut governate Facebook page.
Thousands are killed on the roads each year in Egypt, which has a poor transportation safety record. Speeding, bad roads and poor enforcement of traffic laws cause most of the fatalities.
In 2019, more than 3,400 people died in around 10,000 accidents, according to the country's statistics agency.
The year before, there were over 3,080 deaths and 8,480 car accidents.