The officials said the shell exploded in the small town of Bir al-Abd. At least six others were wounded and were taken to a hospital, they said.
It was not immediately clear who was behind the shelling, which struck the family while they were returning home from their olive farm, according to two residents in the town.
The residents spoke on condition of anonymity out of concern for their safety.
Separately, officials say seven security forces were wounded when two explosive devices hit armored vehicles in Bir al-Abd and the town of Rafah, along the border with Gaza.
The officials spoke on condition of anonymity because they were not authorized to brief the media.
No group claimed responsibility for the attacks.
Egypt is battling an Islamic State-led insurgency in the Sinai that intensified after the military overthrew an Islamist president in 2013. The militants have carried out scores of attacks, mainly targeting the security forces and minority Christians.
Bir al-Abd was the site of a horrific 2017 attack on a mosque by Islamic extremists that killed over 300 worshippers.
The war has largely taken place hidden from the public eye, with journalists, non-residents and outside observers barred from the area. The conflict has also been kept at a distance from tourist resorts at the southern end of the peninsula.
In February last year, the military launched a massive operation in Sinai that also encompassed parts of the Nile Delta and deserts along the country's western border with Libya. Since then, the pace of IS attacks in Sinai's main theater has slowed to a trickle.