A fire department official speaking on condition of anonymity said an electrical short circuit was the most likely cause of the fire, which was so severe that NATO and Afghan army fire squads were called in to help.
"We are all working together to get this under control," the official said. An AFP photographer at the scene said the fire had reduced hundreds of shops to charcoal.
A Kabul police official who also spoke under condition of anonymity told AFP separately that the nearby currency exchange market, the war-torn country's largest, had to be evacuated as the fire approached its outer walls.
"Police helped the money market evacuate and remove their money from the market to safe places," he said.
The Afghan capital, which is home to around five million people, has a poor fire safety reputation, though the fire department was upgraded with international help after the fall of the Taliban regime in a US-led invasion in late 2001.