A number of suspected terrorists were also killed and security forces are combing the area, a statement by the Interior Ministry said.
Islamic terrorists have launched several major attacks, most recently targeting churches in Cairo and other cities with the loss of dozens of lives.
The security sources said authorities were following a lead to a hideout deep in the desert thought to house eight suspected members of Hasm, a group which has claimed several attacks around the capital targeting judges and police since last year.
A convoy of four SUVs and one interior ministry vehicle was ambushed from higher ground by terrorists firing rocket-propelled grenades and detonating explosive devices, a senior source in the Giza Security Office said.
The number of dead was expected to rise, two security sources said.
Two security sources said eight security personnel were injured in the clashes, while another source said that four of the injured were police and four others suspected terrorists.
The Islamic insurgency in the Sinai peninsula has grown since the military overthrew President Mohamed Mursi of the Muslim Brotherhood in mid-2013 following mass protests against his rule.