The clashes broke out on Friday night in Al-Khusus, a poor area in Qalyubia governorate, after a number of children drew a swastika on the walls of a religious institute to which a Muslim man objected, the source said.
The violence escalated into a gun battle with assault rifles between the Muslims and the Christians before security bodies brought the situation under control.
"Five people were killed in the clashes, including four Christians. In addition to this, six others were wounded, at least two of whom were suffering gunshot wounds," the source added.
Security has been stepped up following the violence.
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"The authorities are in complete control of the town," a security official said as the Qalubiya prosecution has started investigating the violence.
Christians form between six and 10 per cent of Egypt's population of nearly 83 million people.
Since the revolution that toppled former president Hosni Mubarak in February 2011, the country's Coptic Christians and Muslims have clashed on several occasions.