The attack comes as President Abdel Fattah al-Sisi fights battles on several fronts. His economic reforms have angered the poor, a bloody crackdown on the Muslim Brotherhood has seen thousands jailed, whilst an insurgency rages in Northern Sinai, led by the Egyptian branch of Islamic State.
The militant group has also carried out deadly attacks in Cairo and has urged its supporters to launch attacks around the world in recent weeks as it goes on the defensive in its Iraqi and Syrian strongholds.
There was no immediate claim of responsibility, but exiled Brotherhood officials and home-grown militant groups condemned the attack. Islamic State supporters celebrated on social media.
The explosion took place in a chapel, which adjoins St Mark's, Cairo's main cathedral and the seat of Coptic Pope Tawadros II, where security is normally tight.