Four "extremists" were also killed, the military said in a statement.
It was the first military death toll announced since the army started its campaign on February 9.
It says it has killed about 60 jihadists and arrested hundreds of suspects since the operation began.
It launched the offensive after Egyptian President Abdel Fattah al-Sisi gave his army commander a three month deadline in November to quash a jihadist insurgency which has killed hundreds of soldiers and policemen.
The group has also targeted Christians, killing more than 100 in suicide bombings and attacks since December 2016.
On Thursday, IS used its al-Nabaa propaganda newsletter to threaten further attacks on Christians and tourists in Egypt.
The group had claimed responsibility for a 2015 Russian airliner bombing that killed all 224 people on board after the plane took off from a southern Sinai resort.
Egypt is holding a presidential election next month, which Sisi is expected to easily win. IS has also threatened attacks on election-related installations.
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