The accident took place in the southwestern region of Jazan, Red Crescent spokesman Bishi al-Sarkhi said in a statement carried by SPA state news agency.
A father, mother and their two daughters died on the spot, while their three sons suffered serious injuries, it said.
A picture published by SPA showed a dead camel lying in a pool of blood in the middle of a road blocked by police vehicles.
Legal experts have called for penalising owners of camels that cause road accidents, Arab News reported in March.