Another two policemen were wounded in the attack near the town of Fakous in the Nile Delta province of Sharkiya north of Cairo, they said.
The identities of the attackers, who fled the scene, were not immediately known but police arrested three suspects in the area.
Sunday’s shooting comes after eight people including six policemen were killed in a bomb blast on Thursday in Cairo.
The explosion in the capital’s Al-Haram district, near the pyramids, came as police raided a flat suspected to be a militant hideout.
An Egyptian affiliate of the Islamic State jihadist group claimed the blast.
Sunday’s attack comes on the eve of the fifth anniversary of the start of the 18-day revolt that toppled longtime dictator Hosni Mubarak.
The authorities have boosted security across the country to prevent attacks and protests, with President Abdel Fattah al-Sisi warning against any form of demonstration on Monday.
Jihadists have regularly attacked security forces since then army chief Sisi toppled Mubarak’s successor, Islamist Mohamed Morsi, in July 2013.
Jihadists say their attacks are in retaliation for a government crackdown targeting Morsi’s supporters that has left hundreds dead and thousands imprisoned.