Six fire engines and around 40 firefighters were called to a fire at a fast food restaurant on Mile End Road in Stepney Green.
A small part of the ground floor restaurant and half of the ducting running from the ground floor to the roof was damaged by fire.
One man left the property before the Brigade arrived. One woman and her baby also left their flat above the restaurant before the Brigade arrived.
Station Commander Justin Randtoul was at the scene, he said: "Motorists are advised to avoid the area while we deal with this incident."
Mile End Road was closed between Burdett Road and Cambridge Heath and remained closed for several hours.
A London Fire Brigade spokesperson said: "We'd like to remind restaurant and takeaway owners to ensure they don't have dirty ducting. If you don't clean 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's 999 Control officers received the first of 11 calls alerting them to the fire at 1343. They mobilised fire crews from Bethnal Green, Whitechapel, Shadwell, Poplar, Millwall and Homerton fire stations. The fire was under control by 1717.
The cause of the fire is under investigation.