The clash occurred after security forces tried to apprehend a group of militants at an abandoned petrol station who were planning “terrorist operations”, the report said.
Those killed included “two of the most dangerous terrorist elements”, the report said, naming them as Mohamed Ibrahim Jabr Shaheen and Jumaa Iyad Marshoud.
Police seized guns and cartridges during the clash, it said.
MENA did not say when the clash took place or give other details about the suspects, and mentioned no casualties among security forces.
Separately, two security officers were killed and four others injured when an armoured vehicle exploded on Sunday night in the border town of Sheikh Zuweid, security sources told Reuters.
Egyptian troops, backed by police, have since February been conducting a major operation against Islamist militants.
Egypt has been fighting an insurgency led by Islamic State and concentrated in the Sinai Peninsula since the Egyptian military overthrew President Mohamed Mursi of the Muslim Brotherhood in mid-2013.