The blasts were heard at around 09:45 local time (07:45 GMT) in the Giza area and were around two minutes apart.
Local media report that the bombs targeted police vehicles stationed near a bridge.
Armed groups have stepped up their attacks in Egypt since the ousting of President Mohamed Morsi by the military in July last year.
A BBC journalist at the scene says there is little obvious damage to the area.
The attacks took place in Giza Square, a regular route for marches against the current government.
Anti-military protests are expected in parts of the capital later, after Friday prayers.
The current government has outlawed the Muslim Brotherhood, declaring it a terrorist organisation. It accuses the movement of supporting attacks against the police and army - a claim the Brotherhood strongly denies.
Since Mr Morsi's overthrow, more than 1,000 people have been killed and thousands of members of the Muslim Brotherhood - where the ousted leader hails from - have been detained in a crackdown by the interim authorities.
Six police officers have been wounded after two bombs went off in Cairo, the Egyptian health ministry says.