Part of a four-roomed flat on the fourth floor of the building was damaged by fire.
Station Commander Jonathon Holt, who was at the scene, said: “Firefighters worked quickly to bring the fire under control.
“One woman was taken to hospital by London Ambulance Service crews.
“There were road closures in place whilst firefighters worked to make the scene safe and buses were on diversion.”
The Brigade was called at 4.56pm and the fire was under control by 5.38pm. Fire crews from West Hampstead, North Kensington, Willesden, Paddington, Kentish Town and surrounding fire stations attended the scene.
The cause of the fire is under investigation.