It is understood Wael Saad admitted killing 64-year-old Bishop Epiphanius with an iron pole at a monastery north-west of Cairo last month.
The Coptic Orthodox leader's body was discovered in a pool of blood on 29th July at the St Makarious Monastery, where he served as an abbot.
Days later, church leaders announced that Mr Saad had been under investigation since the start of the year and he had also been defrocked.
He is currently in detention, pending further enquiries.
The development comes after the Egypt Independent newspaper reported on Saturday that a second monk has been hospitalised after throwing himself from the tallest building in the monastery.
The death of Bishop Epiphanius sent shockwaves through the Coptic Orthodox Church.
Coptic clergy were ordered to shut down their accounts on social media websites like Twitter and monk recruitment has been paused.
Fr Mercurius of the St Makarious Monastery told the Guardian newspaper: "The situation is suffering and agony - we are not able to talk about such things.
"We still don't have a motive announced, though those of us who follow the church affairs closely have become aware of that motive."
Egypt's Christian minority compromises approximately ten per cent of the country's population.
Stay up to date with the latest news stories from a Christian perspective. Sign up to our daily newsletter and receive more stories like this straight to your inbox every morning.