The accident took place late yesterday on Bani Suef-Menya road, about 115 kilometres from Cairo, a statement issued by the Ministry of Health said.
Four other conscripts were also injured during the accident and two of them are in critical condition, the statement added.
Egypt has one of the world's highest accident rates owing to careless driving and poor road and vehicle conditions.
Egypt's President Abdel Fattah el-Sisi assigned a specialist council for community development to devise a complete scheme to minimise road accidents.
The new amendments include a penalty of a minimum of one year in prison for driving under the influence of drugs, and if the driver injures one or more persons he may get at least two years in prison.
The WHO ranks Egypt as the world's tenth worst country in road accidents, after India, China and the US.