The ministry also said that 15 terrorist were killed or injured in the attack.
Security sources on Friday said authorities were following a lead to a militant camp in the desert where eight suspected members of Hasm Movement were believed to be hiding.
Cairo claims that Hasm is the military wing of the Muslim Brotherhood, the most popular political party in Egypt and the oldest in the Arab world. Police forces then launched an operation.
The suspected fighters tried to flee after the exchange of fire there, the sources said, and continued to shoot at a second security unit called in for back-up from atop neighbouring buildings.More news: News On Roman Reigns and Bray Wyatt Being Pulled From WWE TLC
The policemen were killed in the exchange of fire with terrorists late yesterday in el-Wahat desert in Giza governorate, about 135 kilometres from the capital.
Interior Ministry said that a number of policemen were killed and injured, and some terrorists also died in the ensuing crossfire.
While the forces were moving towards the area, they were ambushed by militants who fired rocket-propelled grenades and detonated explosive devices. The Muslim Brotherhood denies this.
Turkish Foreign Ministry on Saturday condemned a deadly shootout southwest of the Egyptian capital, Cairo which left 16 policemen dead on Friday.More news: 'Stranger Things' Star Fires Agent After Sexual Assault Claim
A violent anti-government campaign in the Sinai Peninsula has grown since the military overthrew democratically elected President Mohamed Morsi of the Muslim Brotherhood in mid-2013.
The militant group staging the insurgency pledged allegiance to ISIS in 2014.
Terror attacks in Egypt used to be centered in North Sinai before spreading nationwide and killing hundreds of policemen and soldiers over the past few years.More news: Nuclear War May Break Out Any Moment: North Korea Threatens US Again