Col. Ahmed Mohammed Ali, a military spokesman, told the al-Mesryoon daily a militant group aiming the grenade at a police vehicle on a road near el-Arish missed its target and the missile struck the bus carrying the Egyptian workers.
Dr. Tareq Khater of the Ministry of Health in the northern Sinai said some of the injured workers were in serious condition.
The attack occurred amid reports of plans by the Egyptian army to crack down on terrorists in the Sinai Peninsula
Security in the region has deteriorated since the ouster of Egyptian President Mohamed Morsi earlier this month.
Since then, Egyptian military posts and police and clerics have been attacked by militants and about 37 people have been killed in the Sinai Peninsula, the newspaper said.