Part of a maisonette on the ground floor of a seven-storey block was damaged by the fire. There were no reports of any injuries.
The Brigade was called at 1259pm and the fire was under control by 1.32pm. Four fire engines and around 25 firefighters from Dockhead, Old Kent Road, Dowgate and Whitechapel fire stations were at the scene.
The cause of the fire is under investigation.