The bomb was planted by militants in a car in one of the roads of Al-Arish city and exploded when the security forces passed by it, a statement by the Interior Ministry said.
The injured were transferred to the hospital while security forces are currently searching for the attackers, it said.
In a statement posted on a jihadi website, the Islamic State affiliate in Egypt claimed responsibility for the attack.
Egypt's North Sinai has witnessed many violent attacks by militants since the January, 2011 revolution that toppled ex-president Hosni Mubarak.
Over 600 security personnel have been reported killed since then.
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.