The explosion took place in south Al-Arish city of North Sinai while a police tank was passing by.
The explosive device was planted in the ground by the unknown militants, a security source said.
All the injured persons are in serious condition, a medical source said.
North Sinai has been the scene of many violent attacks by Islamist militants since January 2011 revolution that toppled ex-Egyptian President Hosni Mubarak.
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.