A supermarket worker broke her back when a car drove into her and others outside the store, her colleague said.
A blue Citroen C3 hit pedestrians before driving away from the Tesco car park in Rickmansworth on Sunday.
Police said a woman was taken to Watford General Hospital with serious injuries while a man was treated for slight injuries.
A fundraising page set up to support the victim has already raised nearly four times its target.
A video on social media shows the blue car being rammed by shoppers with trolleys and crashing into other vehicles nearby before it manages to drive away from the store car park.
Police are still trying to find the vehicle and its occupants and confirmed no-one had been arrested.
Julia Matthews, a colleague and friend of the injured woman, set up the fundraising page.
She said: "She shouldn't have had this happen to her ever, but especially not just before Christmas.
"She should be at home with her family, with her partner and her child enjoying the holiday."
Ms Matthews added she hoped the money would help her colleague to enjoy Christmas when she was allowed to go back home.
"I've created this for all those who have asked for a way to help, to help bring some positivity and love into her life when it has been shattered by selfish criminals," she added.
More than £800 had been pledged by 14:00 on Boxing Day.
Officers said the driver and a passenger had been involved in an "incident" inside the store in Harefield Road moments before.
A person was challenged by security staff after allegedly attempting to steal alcohol.
Police said they were examining CCTV from the car park and store after a car was "in collision with several people outside the Tesco store".
A spokesman for Tesco said it was "shocked by the incident" and staff were assisting police with their inquiries.
"Our thoughts are with everyone involved and we are doing everything we can to support our colleague who was seriously injured," he added.