The attack shattered a tense calm in the capital after a spate of bombings on January 24 killed six policemen, in an escalation of a militant campaign following the overthrow of Islamist president Mohamed Morsi.
The interior ministry said two small bombs exploded near policemen stationed on a bridge near central Cairo. At least six were wounded in the attack, the health ministry said.
Police cordoned off the scene, where a lightly damaged police truck appeared to have borne the brunt of the blast.
Police dispersed several protest marches that set off from mosques after noon prayers, security officials said.
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A child was killed and eight other people wounded in clashes between security services and pro-Morsi demonstrators in the village of Elga south of Cairo, security sources said.
The sources said Elga is a stronghold for backers of the ousted president.
And another person was killed in the violence in Fayoum, southwest of the capital.
The country has been shaken by persistent and often violent protests as well as bombings and shootings since the military overthrew Morsi on July 3.
Jihadists based in the peninsula have also claimed responsibility for attacks on police in Cairo and elsewhere.
An Al-Qaeda-inspired group in the Sinai said it carried out a car bombing outside Cairo police headquarters on January 24 that killed four people.
Two more policemen were killed in three additional bombings in the capital that day.