At least seven civilians died when mortars struck the home of a Bedouin family in the village of Negah Shabana, near the border with the Gaza Strip.
It is not clear whether the shells were fired by the militants or troops.
In recent weeks, Egypt's military has stepped up its operation against Islamists in the region.
It is creating a 1km (0.6-mile) deep buffer zone along the border with Gaza by demolishing houses and destroying underground tunnels it says have been used to smuggle weapons from the Palestinian enclave.
The move has displaced more than 1,000 families in the Egyptian town of Rafah and severed an economic lifeline for many Palestinians.
A state of emergency was also declared in North Sinai after 33 security personnel were killed in a suicide bomb attack in the regional capital el-Arish on 24 October.
A night-time curfew has since been imposed, police and army patrols have been increased and additional checkpoints have been set up.
Sinai-based militants have stepped up attacks on soldiers and police since the military overthrew President Mohammed Morsi last year.
Ansar Beit al-Maqdis, a jihadist group that has pledged allegiance to Islamic State (IS) militants in Iraq and Syria, has released a video purporting to show it was behind the attack on 24 October.
It has called on Egyptians to rebel against President Abdul Fattah al-Sisi, the former military chief who led the crackdown on Mr Morsi's Muslim Brotherhood. The Brotherhood has said it rejects violence.
Ten people have been killed in overnight fighting between Islamist militants and soldiers in the north of Egypt's Sinai peninsula, officials say.