According to local media reports, the students on board the vehicle were returning from their classes to their dormitory when the crash occurred, Africa News reports.
A group of ambulances arrived at the area to transport the injured to hospital; the ministry did not specify further details about the condition of those wounded.
The ministry did not state what led to the crash; the driver has been arrested as part of a probe into the accident.
Khaled Abdel-Ghaffar, Minister of Health, and Ayman Ashour, Minister of High Education, have paid their respects to relatives of the students.
Such incidents are not uncommon in Egypt. Every year, road accidents claim thousands of lives in the country. The crashes are mainly the result of bad roads, speeding, and poor enforcement of traffic legislation.
MNA/PR