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."

The company posted net income of $4.9bn (Â£3.4bn) for the fourth quarter, an increase from $4.7bn a year ago.
The announcement sent its share price up 9% in after-hours trading.
That means that Alphabet is now worth around $568bn, compared with Apple which has a value of $535bn.
It is the first time that Alphabet has stripped out the results of its Google business - which includes the search engine and YouTube - from its "Other Bets" business, which includes more experimental ventures such as self-driving cars and internet balloon programs.
The figures show that the "Other Bets" lost $3.6bn in 2015.
But advertising revenue for Google rose by 17% to $19.1bn, in the three months to December as the number of ads, or paid clicks, rose.
Alphabet's claiming of the most value company title has been seen by some as a passing of the technology baton. Google apps and devices compete for market share against Apple iPhones.
The title of most value company in the US has been passed between technology companies for several decades.
Apple became the United States' most valuable company in 2010, when it dislodged Microsoft. Microsoft in turn overtook IBM two decades earlier.
A woman was killed when her scarf got caught in the wheel of a beach buggy she was travelling in.
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Alphabet- Google's parent company- has surpassed Apple as the world's most valuable company after its latest earnings report.