The "takfiri" cell -- an Arabic word for extremists who declare other Muslims disbelievers -- had been meeting when police raided their hideout in Giza province, southwest of Cairo, the ministry said in a statement yesterday.
"When the terrorist cell sensed the police drawing near they began shooting at them, which prompted the police force to fire back," the statement said.
The suspects' affiliation was not immediately clear but police often describe jihadists with links to the Islamic State group or Al-Qaeda as "takfiris".
The Islamic State group's Egyptian branch has killed hundreds of policemen and soldiers in attacks, mostly in the Sinai Peninsula but also in Cairo.
The country has witnessed a deadly insurgency since the military overthrew Islamist president Mohamed Morsi in 2013 and police cracked down on his Muslim Brotherhood movement, killing hundreds of protesters.