The London Fire Brigade said 10 fire trucks and 70 firefighters had been sent to the site shortly after midnight Sunday when a blaze erupted near Camden Stables. It said three floors and the roof of a building within the complex were on fire, AP reported.
Ambulance crews also rushed to the scene, but authorities said no injuries had been reported.
The market is very popular with tourists and Londoners, who are drawn to the area by the shopping and nightlife on offer.
"The fire was moving very fast," said witness Joan Ribes. "People were watching, but we were scared the building could explode at any time since there are restaurants with kitchens nearby."
A different part of the market complex was ravaged by a fire in 2008, and vendors were not able to operate for several months.
Monday's fire came less than four weeks after a fast-spreading blaze engulfed the Grenfell Tower apartment block in west London, killing at least 80 people.
