Footage from the multi-level car park near Sydney Olympic Park showed the man approach the woman before threatening her with the weapon, police said.
The man fled the scene just minutes before police swarmed Uhrig Road in Lidcombe in the city's west about 7.20am on Tuesday.
"Police have responded with a significant response due to the information that a firearm was involved," Auburn Police Area Commander Robert Toynton said.
"Obviously, police take this very, very seriously."
The man was not known to the woman and fled in a white Subaru SUV using fake number plates, police said.
The woman was left shaken but not physically injured.
Heavily armed police, some carrying semi-automatic weapons and wearing camouflage, set up a perimeter around the area, a block of housing units adjacent to the 80,000-seat Olympic stadium.
The man has been described as of medium build, wearing a grey hoodie and a balaclava.
The incident follows a fatal shooting inside a unit in nearby Shale Street on Monday.
Two men have since been charged with the murder of the 38-year-old man, in what police described as a gangland-style attack.
The victim was rushed to hospital about 4am on Monday but died a short time later. A second man was found at the scene with non-life-threatening injuries.
Officers arrested a 21-year-old man on Monday afternoon after a car crashed into a parked vehicle, NSW Police said.
Police found a gun in the car.
Police charged the man with murder and wounding a person with intent to cause grievous bodily harm.
Another man, aged 22 who was arrested in Ermington, was also charged with murder.
Both men were refused bail after facing Burwood Local Court on Tuesday.
Police earlier said they believed the shooting was carried out by offenders with links to organised crime.
"This is a targeted attack. This is not a random attack," Superintendent Toynton said on Monday, before the arrests.
Members of the public have been urged to come forward with any information relevant to either of the incidents.
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