The video, uploaded overnight on social networks, shows an individual telling the camera that he is an Egyptian soldier who was captured in an ambush on an army outpost in North Sinai on April 2.
Attacks claimed by terrorists that day killed 15 soldiers and two civilians near the regional capital of El-Arish, the deadliest assault for months despite a massive army campaign against insurgents on the Sinai Peninsula.
The video then shows the soldier being shot in the head by a masked militant after another unidentified captive is beheaded.
A security official said the soldier's body was retrieved a day after the El-Arish attack.
The Egyptian ISIS affiliate Ansar Beit al-Maqdis has in the past carried out similar execution-style killings in Sinai of people it accused of spying for Israel.
The group changed its name last year to the Sinai Province after pledging allegiance to ISIS, which controls territory in Iraq and Syria.
The group, which has claimed several sophisticated attacks in Sinai and the Nile valley, now wants to establish a province of the self-declared ISIS "caliphate".
After the army ousted "Islamist" president Mohamed Morsi in July 2013, militants claimed a string of deadly attacks against security forces which they claimed were in retaliation for a deadly government crackdown against them.