As mourners exited the Abassiya Church in Cairo, people outside the church threw stones at them, Ahram Online reported.
The mourners then threw stones back and someone fired a gun.
Ahram Online said it was unclear whether the shots fired were live rounds.
It was not reported whether anyone was injured in the clashes.
The funeral taking place at the church was for four Christians killed in fights Saturday between Muslims and Christians in the town of al-Khosous in Qalyubia.
Violence erupted in al-Khosous after a group of Christian teenagers allegedly painted offensive drawings on the gates of a Sunni Muslim institute.
A Muslim also died in the confrontations, Egypt's Health Ministry said.
A number of others were injured and police arrested 15 people, charging them with inciting violence.
Notable deaths of 2014 [PHOTOS]