Ten fire engines and around 70 firefighters were called to a flat fire on Waddington Road in Stratford.
Most of a four-roomed flat on the 12th floor of the building was damaged by fire. One woman was taken to hospital by London Ambulance Service crews.
Station Commander Clive Robinson, who was at the scene, said: "Crews worked swiftly to bring the fire under control and are expected to remain on scene throughout the morning.
"Firefighters wearing breathing apparatus led one woman inside the flat to safety via an internal staircase. She was treated at the scene by London Ambulance Service crews and taken to hospital.
The Brigade was called at 0528 and the fire was under control by 0711. Fire crews from Stratford, Leyton, Poplar, Plaistow, Leytonstone and surrounding fire stations attended the scene.
The cause of the fire is under investigation.