Officer Abdullah Khalil Abdel Gawad Khalil was shot dead by the unidentified gunmen in front of his house in the restive Al-Arish city in North Sinai, a statement by the ministry said.
Search for the attackers has been intensified, according to the statement.
The incident came a day after masked gunmen riding a motorcycle attacked el-Marazik checkpoint killing a policeman and injuring one person.
Egypt's North Sinai has witnessed many violent attacks by militants since the January 2011 revolution that toppled the ex-president Hosni Mubarak.
Over 700 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.