Eight fire engines and around 60 firefighters were called to the fire on Willesden High Road at around 1pm this afternoon (December 13).
The blaze damaged part of the shop on the ground floor and spread to a section of the ceiling between the ground and first floors.
Two people were rescued from the roof by firefighters using a short extension ladder, while five others managed to leave the property before the fire brigade arrived.
Five people were taken to hospital by London Ambulance Service crews.
A 32-metre turntable ladder was deployed at the scene to help monitor the situation.
Firefighters worked to access hard-to-reach areas within the building to bring the fire under control.
Heavy smoke from the fire prompted advice for local residents to keep their windows and doors closed.
The fire led to road closures on Willesden High Road between Bertie Road and Hawthorn Road which currently remain in place.
Crews from West Hampstead, Park Royal, North Kensington, Kentish Town, and Wembley fire stations attended the scene.
The fire was brought under control by 3.21pm, and the cause is now under investigation.
Station Commander Chucks Abili, who was at the scene, said: “Crews worked hard to access the voids and bring the fire under control.
“The fire was producing heavy smoke, so we advised local residents keep their windows and doors closed.
“Willesden High Road is closed between Bertie Road and Hawthorn Road and we’d encourage people to avoid the area this afternoon, particularly as rush hour approaches.”