A gunman opened fire in the Helwan district outside a Coptic church before he was shot dead himself.
They said the exchange of fire also injured three other people.
Egypt's state-run Mena news agency, citing an official at the Interior Ministry, said Friday's attack in the Helwan neighbourhood was carried out by two assailants; one of them fled the scene and was being chased.
A video circulated on social media after the attack apparently shows the dead gunman on the ground.
Authorities have closed off the area around the church.
