The blaze, which broke out on Wednesday evening, also injured 26 people and caused "significant material damage" to nearly 25 shops, the MAP news agency said.
Ten of the injured suffered burns, with three in critical condition, it said. Initial investigations suggest a short-circuit sparked the fire.
Fez's walled city, spanning 280 hectares (about 690 acres), is a popular tourist destination renowned for being one of the best-preserved in the Arab-Muslim world.