The ballot comes after the death of Pope Shenouda III, who headed the church for four decades before his death in March. The new leader will become the 118th head of the Coptic Church.
Whoever is elected to succeed Shenouda will be in charge of leading the region's largest Christian minority through increased sectarian tension in Egypt's post-revolution era.
The council - made up of senior clergy, current and former Coptic officials, journalists, local advisers and MPs - will choose between five candidates: three bishops and two monks. The names of the three receiving the highest number of votes will be written on separate pieces of paper and placed into a box on the altar of Saintt Mark's Cathedral in Cairo.
On November 4, a blindfolded child will select one piece of paper. The new Pope will then be enthroned in a ceremony on November 18.
The five candidates are Bishop Rafael, 54, a medical doctor and current assistant bishop for central Cairo; Bishop Tawadros, 60, of the Nile Delta province of Beheira; Father Rafael Ava Mina, 70; Father Seraphim al-Souriani, 53 and Father Pachomious al-Suriani, 49.
Coptic Christians make up between 6 and 10 percent of Egypt's total population of 83 million. Many are concerned about persecution resulting from the rise of Islamists in Egypt following the election of Mohamed Morsi. This concern comes despite the new president's promise to be a leader "for all Egyptians."
jr/dr (AFP, dpa)