Security officials said they were investigating whether the bomb had been placed on the bus or hurled by an assailant. The victims received mild to moderate injuries, a health ministry official said.
Militants have killed scores of policemen and soldiers in attacks since the military's overthrow of president Mohamed Morsi in July, but this appeared to be the first bombing of a civilian target.
The bombing took place on a busy street in the north Cairo neighbourhood of Nasr City, the officials said.