The car had been involved in a hit and run in Taita on Saturday, which left 37-year-old mother-of-two Anna Chesterfield requiring surgery.
She was on a pedestrian crossing on High St shortly after midday when she was hit by a car whose driver did not stop.
Chesterfield's cousin Nicky Wilton the family were "pleased and relieved" that a person had been arrested for the hit and run.
"As a family we will now focus on supporting Anna with her recovery and thank everyone for their thoughts, prayers, donations and support," she said.
The family had been angry and disturbed after the incident.
"I come from a family where honesty pays, and we always try to do the right thing," she said.
"I would think that people would have the same care that we would, that if something like that happened you would want to stop and make sure that the person was okay."
Local shop owner Kostas Kadrasos said he saw the car moving, then saw Chesterfield lying on the ground.
He said the car turned around slowly before leaving the scene.
Members of the public rushed to help Chesterfield and put a blanket around her as she sat shaking for about half an hour.
The family have created a Givealittle page to support her recovery, which has raised more than $10,000.
Yesterday, Wilton implored the driver of the car to come forward.
"We were pleased that the car has been found, just a bit unfortunate that the driver hasn't been found yet, so hopefully that happens soon," she said.
"It will be weighing on their conscience, so I just implore that individual to hand themselves into police just so that this matter can be resolved and we can get closure for the family."