By Nathan Morley
The blast came just before the Orthodox Coptic Church - which represents 10 percent of the country’s population - celebrates Christmas.
Egyptian government officials said the explosion also wounded a bomb squad commander and another policeman.
The explosive was placed in a suitcase concealed on the rooftop of a building close to the church in the Nasr City suburb in eastern Cairo.
Police are now expected to further tighten security around churches across the country.
As it stands, armed policemen guard churches, and security guards inspect identity cards of those entering churches.
Last month a roadside bomb damaged a tourist bus near the Giza Pyramids. Three Vietnamese tourists and their Egyptian driver were killed.
The so-called Islamic State group has consistently targeted churches and vehicles carrying pilgrims to remote desert monasteries. More than 100 Christians have been killed over the past few years.
Late on Sunday, President Abdel Fattah al-Sisi will inaugurate the Cathedral of Nativity in Egypt's New Administrative Capital, east of Cairo.