It said Abu Duaa al-Ansari was killed in a series of air strikes on fighters of the Sinai Province - or Ansar Beit al-Maqdis - group.
The air strikes targeted jihadist strongholds near the town of El-Arish.
Sinai Province is Egypt's most active insurgent group and has been linked to deadly attacks in Sinai and Cairo.
The Egyptian military said: "The raids left more than 45 terrorists killed, dozens of others injured and several arms caches destroyed."
Brig-Gen Mohammed Samir said in a posting on Facebook that Ansari was killed in an operation guided by "accurate intelligence".
The posting did not say when the operation was carried out.
The air strikes were on southern and south-western areas of El-Arish, the largest town in northern Sinai.
The jihadist group, which has been active in the Sinai peninsula since 2011, has not commented on the army's statement.
Video threat
Islamist militancy has risen in Egypt since the army deposed President Mohammed Morsi of the Muslim Brotherhood in 2013.
Sinai Province: Egypt's most dangerous insurgents
- Originally called Ansar Beit al-Maqdis (Supporters of Jerusalem), but changed its name after it pledged allegiance to so-called Islamic State in November 2014
- Began with rocket attacks on Israel but refocused on targeting Egyptian security forces after the removal of President Morsi
- Its aim is thought to be to take control of the Sinai peninsula to turn it into an Islamist province
- Deadliest attacks include killing of 33 security personnel in North Sinai in October 2014
- The number of active members is believed to be between 1,000 and 1,500
- Believed to have cells in Cairo, Giza and the Western Desert
The group is also a prolific producer of propaganda videos.
On Wednesday, a video said to be from the IS Sinai affiliate issued a rare direct threat to Israel, saying it would soon "pay a high price".