The assailants, riding in two vehicles, opened fire on a security convoy on the main ring road in the Nasr City area.
No group has yet said it was behind the attack, which occurred on Monday night.
However, jihadist militants have killed hundreds of police and soldiers since the military overthrew Islamist President Mohammed Morsi in 2013.
Last month, President Abdul Fattah al-Sisi declared a state of emergency after at least 45 people were killed in suicide bomb attacks on two Coptic Christian churches in Tanta and Alexandria.
So-called Islamic State said a local affiliate had carried out the bombings.
Hours before Monday’s attack, the UN high commissioner for human rights questioned the measures being taken by Egypt’s government to combat jihadism.
Zeid Raad Al Hussein condemned April’s church bombings, but told a news conference in Geneva that the “state of emergency, the massive number of detentions, reports of torture and continued arbitrary arrests – all of this we believe facilitates radicalisation in prisons”, according to Reuters news agency.
“And abetted by the crackdown on civil society through travel bans, freezing orders, anti-protest laws, this is in our opinion is not the way to fight terror,” he added.
“National security yes, must be a priority for every country, but again not at the expense of human rights.”
Human rights activists say more than 1,000 people, most of them Morsi supporters, have been killed and tens of thousands arrested in the crackdown.
