The Rafah hospital said in a statement that the children were killed and wounded during clashes using heavy weapons, with some buried under rubble when buildings were hit and collapsed.
The fighting took place close to the border with the Palestinian Gaza Strip.
Egypt has been hit with a wave of suicide bombings and militant attacks that intensified after the military's ouster of Islamist President Mohammed Morsi in 2013.
The local Islamic State affiliate has claimed responsibility for most of the attacks.
More From This Section
In a statement distributed by IS sympathizers on social media, the militant group said that it had killed and wounded more than 20 soldiers, including senior officers, during the attack.
The Associated Press could not independently verify the claim, but its design and logo resembled previous IS claims.
Egyptian security and health officials had said the attack, just south of the coastal city of el-Arish, killed an army colonel and three soldiers and wounded another 12 soldiers, several of whom were in a critical condition.
Yesterday, New York-based Human Rights Watch said in its annual report that militant attacks across Egypt had increased dramatically in 2015, despite Egypt's commitment of additional security forces.
"The government claimed that the army killed thousands of 'terrorists' in the Sinai but allowed no independent observers into the conflict area, and residents said the army had killed an unknown number of civilians," it said in the report.