It's reported the attack happened on Sunday after local Muslim youths in the village of Tahna al-Jabal in Minya governorate began taunting the seven-year-old son of local priest Metaos Najib Hanna.
The boy's grandfather and his Christian neighbours intervened in the exchange before the Muslim youths attacked them - killing 27-year-old neighbour Fam Khalaf.
The grandfather, the boy and another female neighbour were also injured in the attack.
Egyptian police say four arrests have been made after the incident.
Bishop Makarios of Minya went to visit those affected in Tahna al-Jabal and tweeted afterwards: "Just a reminder, Mr. President, Coptics are Egyptians. Minya is an Egyptian governorate."
His tweet signals wider discontent among Coptic Christians in Egypt who have faced significant persecution of late and feel President Abdel Fattah al-Sissi is failing to adequately protect them.
Al-Azhar, one of the most prestigious Islamic universities in the world, said after the incident: "Al-Azhar followed the media reports regarding a fight between Muslims and Christians because of children in Minya's Tahna El-Gabal village.
"Al-Azhar asserts that the Egyptians are united, and both sides of the fight should adjudicate common sense away from calls aiming to create sectarian strife."
The House of the Egyptian Family, a reconciliation group of Christian and Muslim leaders originally created by Al-Azhar, has been sent to the village to help heal tensions.
This incident comes after Muslims torched five buildings in the village of Abu-Yacoub - also in Minya governorate - over concerns they would be turned into Christian places of worship. 14 people were arrested.
In May, an elderly Christian woman south of Cairo was stripped naked in the street after rumours a Christian man was having an affair with a Muslim woman.
President Fattah al-Sisi promised a full investigation into the incident, in which Christian homes were also torched, but, according to Daily News Egypt, all 16 defendants have now been released.
