Twelve other soldiers were injured while 35 militants arrested in the same day, the statement added.
Egypt army and police have continued "the martyr's rights" operation to the ninth day, with the purpose of eliminating terrorist elements around the restive Sinai towns of Rafah, Sheikh Zuweid and El-Arish, Xinhua news agency reported.
According to Egypt's official news agency MENA, 30 hotbeds were destroyed, 41 explosive devices defused and amounts of ammunition and weapons were seized during the operation.
The army also destroyed two caves, five warehouses, six vehicles and five unlicensed motorcycles used by the terrorists, MENA reported.
Egypt has been battling a surge of anti-security attacks in the restive Sinai Peninsula since the military overthrew Islamist president Mohamed Morsi in 2013, in response to mass protests against his rule.
Hundreds of police and soldiers have been killed, many of whom in attacks were claimed by Ansar Bayt al-Maqdis group, which has changed its name to "Sinai State" and declared allegiance to the Islamic State (IS) militant group last year.
"The martyr' rights" operation came days after the Sinai State released a video documenting its attacks on the military in Sinai, including footage of a wire-guided missile strike that destroyed a navy vessel.
Continuous massive military operations in the peninsula have killed hundreds of militants as part of the country's "war against terrorism," the army said.