The jihadist Sinai Province -- formerly known as Ansar Beit al-Maqdis -- and which has pledged allegiance to the ISIL group, is spearheading an insurgency against security forces on the peninsula since the army ousted president Mohamed Mursi in 2013.
Militants attacked an ambulance carrying a wounded soldier south of the town of Sheikh Zuweid in North Sinai, a hotbed of insurgents, and abducted him, security officials said.
The soldier's body was later found in the area, they said, adding that he had been wounded in a gunfight earlier with militants from the Sinai Province and was abducted while being taken to hospital. A medic was wounded when the ambulance was attacked.
The Sinai Province claimed the killing of the soldier.
"The soldiers of the caliphate stopped an ambulance in an ambush and killed" the wounded Egyptian soldier, the jihadists said on a Twitter account linked to the group.
The Sinai Province has staged deadly attacks against Egyptian soldiers and policemen despite a raft of security measures imposed in the region, including a state of emergency and night-time curfew in parts of North Sinai.
The group says its attacks are in retaliation over a police crackdown targeting Mursi's supporters since his ouster.
Hundreds of Mursi supporters have been killed and thousands jailed in the crackdown. Dozens more, including Mursi, have been sentenced to death after mass trials.