A Kent Police officer fatally shot the woman in the early hours
Kent Police were called after a 37-year-old woman with a gun was seen in the centre of Sevenoaks at 0120 BST.
Armed officers shot the woman, who has not been identified but was from the Sevenoaks area. She was given first aid at the scene but pronounced dead.
Part of the centre of the town, including the bus station, was sealed off following the incident.
The Independent Police Complaints Commission (IPCC) said an investigation would be carried out.
Whenever there is a fatal shooting by police our independent investigators go to the incident immediately
Nicola Williams, IPCC commissioner
The victim is believed to be the first woman to have been shot dead by police for at least 27 years.
Two residents in Sevenoaks told BBC News 24 that they were woken up at about 0300 BST by barking dogs and a "commotion".
They then described hearing a loud bang.
Officers and forensic science experts have been searching the rear car park of a department store based in Sevenoaks High Street.
A firearm was recovered at the scene.
IPCC commissioner Nicola Williams said: "I send my sympathies to the woman's family and friends and also the police officers concerned.
"Whenever there is a fatal shooting by police our independent investigators go to the incident immediately."
Accidentally shot
She added that it was "unusual" for a woman to be the victim, and that the shooting had not been part of a wider police investigation.
Three other women have been shot by police in the last 27 years.
In 1980, Gail Kinchen was accidentally shot dead by a police marksman during a siege in Birmingham.
Two other women have been wounded in police shootings.
Cherry Groce was left paralysed after she was accidentally shot by police in 1985 during a raid on her home in Brixton, south London.
In 1997, Jane Lee was shot in Ilford, Essex, by police investigating a firearms incident. She was taken to hospital and recovered.
Map highlighting Sevenoaks, England.
A woman, reported to be an expert in martial arts, has been shot dead by police in a car park behind ''M&Co'', a women's clothing shop in Sevenoaks, Kent, England. According to reports, the woman pulled a gun on police who then shot her.

"I can confirm that in the early hours of this morning Kent Police fatally shot a person. This has been referred to the IPCC which has a team of investigators now at the scene," said a spokesman for the Independent Police Complaints Commission (IPCC).

A bus station in Sevenoaks was shut down and closed off to the public while police investigated the incident. A tent was placed over the crime scene to ensure that evidence was kept intact.

Regular police officers do not carry guns in the United Kingdom. Special officers are dispatched to scenes with guns only if situations become serious or dangerous.