Four fire engines and around 25 firefighters were called to reports of smoke coming from the roof of an office building and restaurant on Houndsditch in The City.
A small part of the extraction system from the basement to the roof of the building was damaged by fire. Seven people left the building before the Brigade arrived. There were no reports of any injuries.
The Brigade's Fire Investigators believe the fire was caused by the ignition of grease and fat deposits within the extraction system, following charcoal being used in a tandoor oven in the restaurant kitchen.
A London Fire Brigade spokesperson said: "The alarm was raised when a member of the public saw smoke coming from the roof of the building and called the Brigade.
"On arrival, firefighters found the extraction system from the kitchen of a restaurant in the basement of the building was alight. Crews worked to contain the fire to the extraction system and prevent further damage.
"We'd like to remind restaurant and takeaway owners to ensure they don't have dirty ducting. If you don't clean the ducting in your extraction system regularly, you're at a greater risk of ducting fires.
"You should also make sure you keep the hob, cooker hood and extractor fan clean too – built up fat and grease can ignite and cause a fire."
The Brigade was called at 1010 and the fire was under control by 1234. Fire crews from Whitechapel, Dowgate, Shoreditch and Shadwell fire stations attended the scene.