The four men were killed in the blast south of Al-Arish city, security and health officials said.
The 12 injured, some of whom were in critical condition, were transferred to hospital for treatment.
Security forces have cordoned the area and were searching for attackers, officials said.
Egypt's North Sinai has witnessed many violent attacks by militants since the January 2011 revolution that toppled president Hosni Mubarak.
The attacks targeting police and military increased after the ouster of Islamist president Mohamed Morsi in 2013 by military following massive protests against his rule.
The military has launched security campaigns in the area, arrested suspects and demolished houses that belong to terrorists, including those facilitating tunnels leading to the Gaza Strip.