Three other conscripts were injured during the exchange of fire with the militants in Al-Arish city late last night.
The militants targeted a group of policemen and killed five of them. Security forces have cordoned off the area and are searching for the attackers, the ministry said in a statement.
The Islamic State terror group claimed responsibility for the attack in a statement posted on jihadist websites.
The attacks targeting police and military personnel increased after the ouster of Islamist president Mohamed Morsi in 2013 by military following massive protests against his rule.
More than 700 security personnel have been killed and over 18,000 have been injured since 2011.
The military has launched security campaigns in the area, arrested suspects and demolished hideouts of the terrorists, including those facilitating tunnels leading to the Gaza Strip.
