The soldier was killed in the town of Sheikh Zuweid, where jihadist militants have been active despite a sweeping army crackdown.
His death came two days after a kidnapped policeman was found shot dead in the northern part of the peninsula, a jihadist hub.
The most active jihadist group in Sinai, Ansar Beit al-Maqdis, has pledged allegiance to the Islamic State group that controls swathes of Syria and Iraq.
Militants have killed scores of policemen and soldiers since the army overthrew Islamist president Mohamed Morsi in 2013 and cracked down on his supporters. -AFP