The clashes erupted in the poor district of Moqattam mid-afternoon Tuesday when at least 1,000 Christians gathered there to protest the burning of a church last week.
Fighting broke out when dozens of Muslims arrived in the area, which is inhabited by Copts who work as rubbish collectors and who had blocked a main north-south artery in the capital.
Some Muslim crowd members opened fire on the demonstrators, a Coptic priest told French press agency AFP, adding that they had also petrol-bombed local houses and workplaces.
People on both sides threw stones and soldiers at the scene fired shots into the air in a bid to disperse the crowds, according to witnesses.
Ahead of the clashes, Copts had protested in central Cairo against the burning of a church south of the capital after deadly clashes between Christians and Muslims.
The protest outside the radio and television building came a day after at least 2,000 angry Christians demanded that the torched church be rebuilt, and that those responsible be brought to justice.
On Monday, Egypt's ruling military council vowed to have the church rebuilt and to prosecute those behind the arson attack.