The bomb exploded close to an armoured vehicle on a highway near El-Arish, the provincial capital of North Sinai, it said in a statement.
Islamist militants have killed hundreds of soldiers and policemen in attacks in the peninsula.
On Sunday, gunmen killed two members of the security forces in an ambulance as they were being taken to hospital with injuries from a bombing. A medic was also shot dead.
Most of the Sinai attacks are claimed by the Islamic State jihadist group's Egyptian branch, "Sinai Province".
Sinai jihadists pledged allegiance in November 2014 to IS, which controls parts of Iraq and Syria and also has a presence in conflict-ridden Libya.
Jihadists, who have long used Sinai as a base, launched an insurgency after the military overthrew Egypt's Islamist president Mohamed Morsi in 2013.