Naija “Naija” Mooi, Princess of Wales’ sister, was rushed to Royal Preston Hospital on Thursday morning.
The princess was in a serious condition, the hospital said in a statement.
Naijas mother, Prince Harry, was also rushed to the hospital.
Princess Naiji and Prince Harry were both in the hospital at the time of the accident.
The Queen has since been released.
Prince Harry’s office said Princess N, who has a long history of health issues, was “unstable”.
“She was discharged yesterday and will return home tomorrow,” the office said in an emailed statement.
The Princess has been in intensive care since Thursday morning after she suffered a “significant head injury” in a car accident in Birmingham on Thursday night.
The Crown Prosecution Service (CPS) said she had suffered a fractured skull, bruising to her spine, and internal bleeding in her brain.
It also said she suffered from “multiple fractures of the skull and neck”.
It is understood the Princess has not been formally assessed by a doctor but her family has spoken to doctors and is receiving treatment.
Police have launched a criminal investigation into the accident and the matter is being treated as a “serious accident”.
Police said Princess Harry and Princess N had been in a Mercedes Benz in the driveway of a home on Parnell Street, Birmingham, at about 9.20pm on Thursday when the incident occurred.
A white Mercedes car drove through the gate of the house and then stopped, and the Princess was inside, according to the CPS.
Police said a woman driving the Mercedes tried to pull the Princess from the car, but she resisted and was punched.
Police are treating the incident as a serious accident.
There was a large crowd in the street at the scene.
The incident happened on a busy street with several houses nearby and it is not known how many people were in the area at the moment.
Police say the Princess, who is now in hospital, has a history of serious health issues.
Police also said they were investigating the possibility that the driver of the car may have been drunk.
It is unclear whether the incident is related to the Princess’s engagement to the prince.
The car was reported stolen on Thursday and officers have launched an investigation.
The royal couple are currently on a trip to New Zealand.
The CPS said it would make a statement in due course.
Police were called to the scene of the incident after a passer-by reported seeing the Princess “suddenly fall from the back seat of the vehicle” and being dragged by the vehicle’s bumper.
The girl was taken to Royal Hospital in Birmingham and has been treated.
Police and ambulance crews are investigating the incident and are treating it as a suspicious incident.
The Royal Palace was closed in honour of the Queen.
The couple will return to England next week for a week-long visit.
The Duchess of Cornwall, the Duchess of Cambridge, and Prince William, Duke of Cambridge are also due to visit Birmingham on Tuesday.
The Duke of Edinburgh and Duchess of York will also visit Birmingham.
The Prince of Wales and Duchess Kate Middleton will be in Birmingham for the next week, the royal couple have confirmed.