The bomb, planted by unknown militants in Al-Arish city, exploded when an armoured police vehicle was nearby, officials said.
The injured were admitted to a hospital as security forces searched the area for the attackers.
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 belonging to terrorists, including those facilitating tunnels leading to the Gaza Strip.