The interior ministry said in a statement that the explosion took place next a checkpoint, killing two officers
The attack occurred in the western Talibiya neighbourhood of the capital, shortly before Muslim Friday prayers and when Cairo's streets are mostly empty.
The bloodied bodies of several policemen could be seen at the blast site next to police vehicles that had been stationed there, an AFP photographer reported.
Police cordoned off the area with yellow tape as they searched for more explosives.
The interior ministry said in a statement that the explosion took place next a checkpoint, killing two officers, a low ranking policeman and three conscripts.
The bombing also wounded three conscripts.
There was no immediate claim of responsibility for the attack.
Militants have repeatedly attacked policemen and soldiers since the army overthrew Islamist president Mohamed Morsi in 2013 and unleashed a bloody crackdown on his followers.
Most of the attacks are conducted in the Sinai Peninsula by a branch of the Islamic State group, which has killed hundreds of soldiers and policemen there.
But militants have also targeted security forces and government officials in the capital.
An Egyptian judge in one of the trials of Morsi, who was detained after his ouster, escaped unharmed last month when a car bomb exploded as he drove by.
That attack came days after a roadside bombing targeting a police convoy killed a passerby.
In September, militants set off a car bomb as the country's deputy state prosecutor was passing. He too escaped unharmed.
Most of the Cairo attacks in recent months have been claimed by two little known militant groups, Lawaa al-Thawra and the Hassam Movement.
Police say they are affiliated with Morsi's Muslim Brotherhood movement, which was banned months after his overthrow and listed as a terrorist organisation.
The Brotherhood, which espoused grassroots work and change through elections, denies it is involved in violence.
The group had been the country's largest opposition movement under veteran strongman Hosni Mubarak and dominated polls after his overthrow in 2011.
In 2012, it won a presidential election with its candidate, Morsi, whose divisive rule led to mass protests a year later that prompted the army to overthrow him.
Hundreds of his supporters were killed in protest clashes with police and the army in the following months.
The Brotherhood now operates as an underground and splintered movement, with some of its followers believed to have embraced attacks against policemen while others insist on non-violence.
Friday's bombing came days after the interior ministry said police killed three members of the Hassam Movement in the country's south, and weeks after it announced breaking up one of the group's cells.