The bomb planted on a pavement exploded as the public bus passed by in the northern district of Nasr City, a security source said.
A second bomb found in the area was defused by police.
Bombings in Cairo have so far not been a feature of the ongoing confrontation between security forces and ousted president Mohammed Morsi's supporters in the Muslim Brotherhood.
The explosion came after Egypt's government designated the Brotherhood a terrorist organisation, and two days after a bombing at a police headquarter in northern Egypt killed at least 15 people.
The location of the explosion is near Al-Azhar university building, the headquarters of National Security as well as a police station.
The area was cordoned by the police for investigations.