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.