The family were asked to stay out of their home until the fire was brought under control. It took firefighters from seven trucks more than an hour to do so.
It was the second time this year a car had hit the row of shops, which also includes another dairy, a takeaway and a liquor store.
Police asked anyone who saw the red Ford Falcon shortly before it crashed, or who had any related information, to contact Constable Glen Carlyle on (09) 261-1300.
The fiery crash was the first of two fatal accidents yesterday.
In the other, a person died when a car struck a tree in South Taranaki.
A St John Ambulance spokesman confirmed the death, on Patiki Rd, Pihama, shortly before 3pm.
Another person in the car suffered minor injuries but refused care.
In Christchurch, a man, who blew 829mcg - more than three times the breath-alcohol limit of 250mcg - crashed into a house in New Brighton.
Emergency services were called to the accident on Marine Parade at 4.40am.
He was tested by police and charged with drink-driving.
Shortly after midnight yesterday, a pair of teenagers also crashed into a house in Hamilton as they attempted to flee police in what was believed to be a stolen car.
Officers were chasing the silver Toyota Altezza sedan when the driver lost control as the car was going through the intersection of Heaphy Terrace and Clarkin Rd.
The house suffered extensive damage, and the residents were quite shaken, but no one required medical attention.
Senior Sergeant Robbie Hermann of the Waikato police district command centre said the two people in the car tried ran away after the crash, but one was caught by police and arrested.
A 15-year-old was charged with failing to stop for police and was to appear in court today.
They were still making inquiries about the other person who ran away.
In Napier, two cars crashed at the intersection of State Highways 2 and 5, locally known as the Taupo turnoff on the Napier-Wairoa road.
Police said one of the cars turning into SH5 failed to give way to an oncoming vehicle, causing minor injuries to the seven occupants of the cars - including one teenager and a pregnant woman.
And in Wellington, police arrested a man after a dramatic hour-long chase around the central city.
The man took after crashing a vehicle on Jervois Quay.
- Staff reporters