Around 70 firefighters and officers were called to the scene at just before midnight on Sunday evening.
London Fire Brigade said that no injuries were reported but that the upper floors and roof of the building were damaged.
Camden Market said in a statement: “An isolated fire broke out in a building adjacent to the market hall area of Camden Lock Market overnight which was brought quickly under control by the Emergency Services and we are now working closely with them to investigate the cause. Thankfully no one was injured during the incident.
“While a small section of Camden Lock market will be closed off to the public until further notice as a precaution, the rest of Camden Lock market and the wider area, including Stables Market and Union Street, will be fully open and operating and welcoming visitors and customers as usual today.”
The market area has been hit twice by fires in recent years, in 2008 and 2014.
The cause of last night's fire is still under investigation.