A statement said security personnel clashed with the alleged militants during an operation to comb a remote area some 400 kilometres south of Cairo.
Five "terrorist elements" were killed after they opened fire on security forces, the ministry said.
There was no mention of any losses among the security personnel.
Islamic State claims responsibility for Egypt's Sinai attack
Extremists launched an insurgency in Egypt after the 2013 ouster of president Mohamed Morsi, who was forced out by the military in the face of mass protests against his rule.
Attacks have largely been concentrated in the Sinai Peninsula in eastern Egypt, but have also taken place elsewhere across the country.
The army in February launched a major operation centred on the Sinai to wipe out extremists, including members of the Islamic State group.
The military says that over 250 suspected extremists and at least 35 soldiers have been killed in the "Sinai 2018" operation.
President Abdel Fattah al Sisi has made the fight against terrorism a priority, but rights groups accuse the government of also using it as cover to crack down on dissent.
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