The violence was triggered by a feud between two families. It erupted over a romantic relationship between a Christian man and a Muslim.
It culminated in fighting on Friday in which both of the couples' fathers were killed, another security official said.
After the funeral for the woman's father on Saturday, a group of Muslims headed to the village church and set it on fire.
The army, managed to put the fire out and restore calm to the area, the official said.
Coptic Christians make up about 10 per cent of Egypt's population and have been subject to sporadic sectarian violence. Marriage between a Christian man and a Muslim woman is illegal in Egypt unless the man converts to Islam.