One child is reported to be in critical condition. Another child and four adults, including the driver of the car, are among the six people taken to hospital.
London police said the incident took place around noon ET.
Witnesses inside the store said they heard a car engine revving before a red sedan hit the glass doors.
Police said the car reversed and went through the front door, with the car ending up completely inside the store.
The store has been closed for the day as police continue to investigate the incident.