The bomb was planted by unknown militants in Sheikh Zwayied area of the province which is usually used by security forces, the Youm 7 news website reported.
Three other army personnels were injured during the explosion, the military said.
Yesterday, seven militants were killed in different parts of Sinai during army raids, they added.
Egypt's Sinai has witnessed many violent attacks by militants since the January 2011 revolution that toppled the ex-president Hosni Mubarak.
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Over 500 policemen and soldiers, have been killed in the attacks.
Militant groups claim their attacks are in retaliation for a government crackdown targeting Morsi's supporters that has left hundreds dead and thousands jailed.
The government declared a three-month state of emergency and a curfew in different parts of Sinai following a terror attack that left at least 31 Egyptian soldiers killed in October.
The army 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.