Part of a flat on the fourth floor of a five-storey block was damaged by the fire. One woman left the affected flat before the Brigade arrived. She was treated at the scene for smoke inhalation by London Ambulance Service crews and taken to hospital.
The Brigade was called at 1.18pm and the fire was under control by 2.35pm. Six fire engines and around 40 firefighters from Whitechapel, Bethnal Green, Plaistow, Dowgate and East Greenwich fire stations were at the scene.
The cause of the fire is under investigation.