The bus was traveling over a crossing where lights and a siren warned of the approaching train, Ahram Online and the Middle East News Agency reported.
The crash occurred near the village of Manfalout in the Assiut governorate of Upper Egypt.
Eighteen school children were injured, seven critically, Assiut's governor said.
All of the children on the bus were reported to be between the ages of 4 and 6.
The bus driver, who was among the dead, drove over the crossing despite the warnings and in full view of a crossing guard and a traffic policeman, the railway authority said in a statement.
Abdel-Meguid Mahmoud, Egypt's prosecutor-general, has ordered an investigation of Mohamed Rashad El-Metiny, the minister of transportation; Mostafa Qenawi, the head of the railway authority; and the crossing guard.
Metiny and Qenawi have submitted their resignations.
An eyewitness, Osama Seddik, said it took police 2 hours to arrive at the scene and only one ambulance was sent.
Recovery of the bodies was hampered by people blocking the road, looking for their children, he said.
Seddik charged that the crossing guard was asleep as the train approached.