Egypt's official MENA news agency said an assailant lobbed a bomb into a chapel close to the outer wall of St Mark's Cathedral, seat of Egypt's Orthodox Christian church and home to the office of its spiritual leader, Pope Tawadros II, who is currently visiting Greece.
Egyptian state TV and the Health Ministry gave the casualty toll.
Witnesses said the explosion may have been caused by an explosive device planted inside the chapel. Conflicting accounts are common in the immediate aftermath of attacks.However, a security official, speaking on condition of anonymity, said that the blast had been caused by an explosive device likely thrown by an unknown person inside the church.
There was no immediate claim of responsibility for Sunday's attack, which has drawn a flurry of condemnations by government and religious leaders as well as assertions of unity between Egypt's Muslim majority and Christians, who account for about 10 percent of the country's 92 million people.
An angry crowd of several hundred people gathered outside the cathedral, chanting anti-government slogans and calling for the sacking of the interior minister, who is in charge of security. Scuffles broke out with the police when the protesters tried to push through their barricades, but there were no immediate reports of arrests. Police in full riot gear later arrived at the scene.