The breakdown of military casualties was not immediately clear. However, two security sources told Reuters that the some of the injuries were serious.
Security forces launched a campaign a year ago against Islamist militants focused on Egypt's Sinai peninsula, and say they have killed several hundred militants since then.
"Combing operations and the pursuit and elimination of the terrorist elements in the area where the incident took place is ongoing," the military spokesman said in a statement.
The security sources said operations were taking place under aerial cover.
Since 2013, Egyptian security forces have battled Islamist militants, who have repeatedly targeted security checkpoints and Egypt's Christian minority.