Officers were called to the building, which houses a tattoo parlour and residential accommodation, on Lancaster Road, in Enfield, at 0530 BST.
Neighbouring properties have been evacuated and police are searching the rubble to see if anyone is trapped.
Police are treating the incident as suspicious, but not terrorist-related.
Suspect car
One man and two women suffering serious burns, which are not thought to be life-threatening, were taken to hospital.
People from neighbouring properties have been moved to local authority accommodations.
Police said a cordon has been placed around the scene and the road will remain closed for the weekend.
Officers are appealing for information about a red Mark 3 Escort, which was seen leaving the scene and going towards Lavender Road between 0500 and 0600 BST.
A 35-year-old man was spotted running away from the building and joining another man in the car before they left the scene.
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