She was a passenger in a white Skoda driven by a man in his 80s when the car hit three cars and a minibus before colliding with the wall of the supermarket in Hungerford.
The crash happened at around 17:00 GMT on Thursday. The woman from Marlborough was taken to hospital and died the following day.
The driver sustained minor injuries.
A woman in her 80s has died after a crash involving four vehicles in a Tesco car park.