Fifteen militant were also killed in the fighting, the military said in a statement, without saying when the incidents took place.
The military said the clashes broke out when soldiers raided "an extremely dangerous" militant hideout.
Two Turkish soldiers killed in Al-Bab attack
The Islamic State group had said in a statement on Wednesday afternoon that it blew up two army vehicles during clashes south of the Sinai city of El-Arish.
The terrorists have killed hundreds of soldiers and policemen since the army overthrew president Mohamed Morsi in 2013 and cracked down on his supporters.
Former Egyptian president Hosni Mubarak to be released, claims lawyer
The attacks have mostly been confined to Sinai, which borders Israel and the Palestinian Gaza Strip, but the militants have also struck elsewhere.
In October 2015, the group claimed responsibility for bombing a Russian airliner carrying holidaymakers from a south Sinai resort, killing all 224 people on board.
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