All of the people killed were members of one family, two of them were children, Sputnik News reported.
The attackers blew up a bomb-laden car near a residential house located next to a police station in Arish, the capital of the North Sinai Governorate.
Nobody has claimed responsibility for the attack, which could nonetheless be a terrorist act, according to law enforcement.
Egypt has been conducting anti-terrorist operations in North Sinai for the last two years, amid the rise of extremists in the region, particularly the "Sinai Province" ("Wilayat Sinai") militant group, known as Ansar Bait al-Maqdis before its members took an oath of allegiance to the radical ISIL group in the fall of 2014.
Ansar Bait al-Maqdis emerged after the 2011 Egyptian revolution, which forced former dictator Hosni Mubarak out of power after an over 30-year rule. The militants aim to topple Egypt’s current government.
In August, Egyptian President Abdel Fattah Sisi signed a tougher and controversial anti-terrorism bill into law to combat the recent spike in attacks on the Sinai Peninsula.