Six fire engines and around 40 firefighters were called to a fire at a flat on Mile End Road in Shadwell.
Part of a six roomed flat on the fifth floor was damaged by fire. One woman and a child were treated on scene by London Ambulance Service crews for smoke inhalation.
The Brigade was called at 1116 and the fire was under control by 1207. Fire crews from Homerton, Bethnal Green, Whitechapel, Shadwell, Shoreditch and Dockhead fire stations attended the scene.
The cause of the fire is under investigation.