The collision happened near to the Jubilee clock in the junction of Harlesden High Street and Wendover Road, at about 2pm after the route 18 bus lost control and careered into the shop front.
The injured were transferred to hospital following the incident with three who were seriously injured, with one person treated at the scene.
One witness, who wished to only be known as Harry, told the London Evening Standard there were “about a hundred” emergency services crew at the scene and an air ambulance also attended.
London Fire Brigade said 20 people were helped out of the bus and 45 people evacuated from nearby buildings.
“I saw windows being smashed at the back of the bus’s top deck to enable people to jump to safety” another witness told BBC.
The damage property is believed to be a jewellery shop named Waves and the four people inside had to be rescued by firefighters using ladders at the back of the building.