Part of the first floor of a split level maisonette, on the seventh and eighth floor, was damaged by fire.
The Brigade was called at 4.16.pm and the fire was under control by just after 5.30pm.
There were no reports of any injuries.
Fire crews from Millwall, Plaistow, Shadwell, Whitechapel and surrounding stations were at the scene.
The cause of the fire is under investigation.