A woman armed with a knife has been shot dead by police officers after she lunged at them outside a fast food outlet in Sydney's south-west.

The shooting took place just before midday on Tuesday outside the car park of Hungry Jack's on the corner of Hoxton Park Road and Cowpasture Road in West Hoxton

Police said officers used capsicum spray to try and subdue the woman before firing one shot, which hit the 22-year-old woman in the chest.

Officers carried out CPR on the woman but she died shortly afterward.

Armed officers surround the woman moments after she was fatally shot at West Hoxton. ( Twitter: TEN Network )

NSW Assistant Police Commissioner Frank Mennilli said the critical incident team would now investigate the decision to shoot by officers.

"A number of tactical things were used [in the incident]. I was informed capsicum spray was utilised," Commissioner Mennilli said.

Witnesses reported hearing two shots fired, but Commissioner Mennilli said information supplied to him suggested just one shot was fired at the woman and it was fatal.

"The officers are distraught. This is a tragic situation," he said, adding that police were still trying to contact the woman's family.

Local resident Alan Sobbi said he saw the incident from the balcony of his home.

"We saw two police officers talking to a woman, yelling, and then she approached them with something and we heard bang bang," Mr Sobbi said.

"After that police came from all over the place and we didn't know the woman was shot dead until later.

Sorry, this video has expired Police used 'a number of tactical options' against knife-wielding woman

"So we heard the shots and saw her attacking the police.

"She moved forward to the police. I couldn't see if she had anything in her hand or not, but she was moving towards the police.

"When we heard the gunshots we thought, 'is this a movie?'

"We never thought someone was going to get shot."

The critical incident team investigating the shooting will comprise members of the State Crime Command's Homicide Squad and investigators from South West Metropolitan Region.

The investigation will be overseen by the Professional Standards Command.