The incident took place yesterday on the ring road in the governorate, about 245 km south of Cairo.
Following the accident, ambulances rushed to the spot. The two injured persons, stated to be in critical condition, were immediately taken to a nearby hospital, local media reported.
Road accidents are common in Egypt. Earlier this month, two major accidents occurred in different governorates, killing at least 28 people.
Taking note of the accidents, President Abdel Fattah el-Sisi assigned a specialist council for community development to devise a complete scheme to minimise such accidents.
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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.
Egypt has one of the world's highest traffic accident rates due to careless driving, condition of roads and vehicles.
A recent report by the Central Agency for Public Mobilization and Statistics said 15,578 car accidents took place in Egypt in 2013, up 0.4 per cent from the year before, which claimed the lives of 6,716 people and injured 22,411 others.