The attack happened close to Saint Catherine's monastery
The attack was targetting security forces and comes days before Pope Francis is due to be visiting the country.
The shooting was carried out by a gunman and happened at a security checkpoint a few hundred metres from the church entrance, according to a security source.
The injured have been taken to Sharm el-Sheikh international hospital for treatment.
No group has claimed responsibility.
The monastery, which is visited by thousands of tourists annually, is one of the oldest working monasteries in the world.
The attack comes a week after two bombings on churches claimed by Daesh killed 45 people.
Attacks are common in northern Sinai, where an insurgency by Islamist militants has raged for years, but rare in south Sinai.
The monastery is a UNESCO World Heritage Site
Pope Francis is due to travel to Egypt later this month to promote better relations between Catholics and Muslims.
The Pope has accepted an invitation to visit Cairo from President Abdel Fattah al-Sisi, Roman Catholic bishops, the leader of the Coptic Orthodox church of Alexandria and the grand imam of Al Azhar mosque.
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