Four fire engines and around 25 firefighters tackled a flat fire on High Road in Willesden Green.
Half of the ground floor of a split-level flat was damaged by fire. Eight people left the building before the Brigade arrived and a baby was taken to hospital.
The Brigade was called at 0624 and the fire was under control by 0803. Fire crews from Willesden, West Hampstead and North Kensington fire stations attended the scene.
The cause of the fire is under investigation.