The market is adjacent to the famed Al-Hamidiyeh souk in one of the world's oldest cities.
"It began at 06:00 am in one shop in the centre of the neighbourhood and then spread to other shops," a senior civil defence member in the market told AFP.
Speaking to the official SANA news agency, the capital's civil defence chief General Jihad Mousa blamed an electrical fault.
An AFP correspondent said at least 50 store fronts and warehouses were damaged.
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Syria's economy has already been devastated by the five-year war, with its foreign reserves depleted and inflation soaring.
"Our livelihood has gone," said one shopkeeper after Saturday's blaze, his head in his hands. "This shop used to feed ten people who worked for me."
An AFP correspondent said the owner of the shop where the fire started was taken to hospital with severe burns to his head and hand.
Firefighters tried to douse the flames from within the souk's alleyways and from rooftops.
Toy shop owner Mohammad Ashqar said he had restocked his store just two days before the fire.
"I haven't been able to go in yet to check on the shop," he said.