The accident took place when the bus collided with the vehicle near Karam Omran village in the Upper Egyptian city of Qena, police said.
Three people were killed and 28 others, including a policeman, were injured. Ten ambulances reached the spot and transferred the injured to a nearby hospital, they said.
Egypt has one of the world's highest accident rates due to careless driving and poor road and vehicle conditions. The WHO ranks Egypt as the world's tenth worst country in road accidents, after India, China and the US.