Four fire engines and around 25 firefighters were called to a flat fire on Commercial Road in Whitechapel.
Part of a one-room flat on the fourth floor of the building was damaged by fire. One person was treated on scene by London Ambulance Service crews after suffering from smoke inhalation.
The fire is believed to have been accidental and caused by combustible items being too close to an electric heater.
A London Fire Brigade spokesperson said: “Fires involving heaters like this are all too common. They usually start when items, like clothes or bedding, are placed too close to the heater and ignite.
“It’s absolutely vital that heaters are kept well away from curtains, bedding or furniture and are never used to dry clothes.
“It's also important to always sit at least a metre away from the heater, as it could set fire to your clothes or your chair and position them where they won’t be knocked over."
The Brigade was called at 0449 and the fire was under control by 0610. Fire crews from Whitechapel, Shadwell, Shoreditch, Bethnal Green and Dowgate fire stations attended the scene.