Sixty-two-year-old Gillian Sandle, was a passenger in the vehicle which was travelling through Havant, near Portsmouth, on Sunday lunchtime.
Members of the public tried to revive her, but she died in hospital.
Ms Sandle's family said they were "totally devastated at the sudden and tragic loss of such a wonderful lady".
Police are appealing for witnesses to the accident in North Street between 12:35 and 12:40 GMT.
The vehicle was a blue Volkswagen beach buggy.
Sgt Melanie Adcock of Hampshire Constabulary said: "This incident took place at a busy time of day when there were lots of Christmas shoppers in North Street so it is likely many people saw what happened.
"I would like to hear from anyone who witnessed any part of this incident."
A woman was killed when her scarf got caught in the wheel of a beach buggy she was travelling in.