The incident took place last night in Al-Arish area. The car was parked in front of a take-away restaurant near a hotel in El-Bahr street. Several houses, cars and commercial shops in the area were damaged due to the explosion.
Following the incident, army officials cordoned off the area and launched an investigation. A bomb disposal team rushed to the spot in search for other bombs.
The explosion took place during the curfew hours, a police official said.
The army has launched frequent security operations in the area, arrested suspects and destroyed terrorist bases including tunnels leading to the neighbouring Gaza Strip.
North Sinai has witnessed many violent attacks by militants since the Egyptian Revolution of 2011, that toppled ex-president Hosni Mubarak.
The militant attacks targeting police and military increased after the ouster of Islamist ex-president Mohamed Morsi last year. Over 500 security personnel have been killed so far.