The tree fell on the car on Raby Road in Leppington, in the city’s south-west, around 4pm this afternoon.
The rescuers rushed the women to hospital and it’s believed she is in a stable condition.
The Bureau of Meteorology (BoM) issued a thunderstorm warning for damaging winds and large hailstones.
Severe thunderstorms were detected on the weather radar at 3.25pm near Erskine Park and St Marys in Sydney’s west.
“These thunderstorms are moving towards the southeast,” the BoM said.
“Damaging winds and large hailstones are likely.”
The BoM said the thunderstorms are moving to the south-east.
They are forecast to affect waters off Royal National Park in Sydney’s south as well as Stanwell Park and Thirroul in the Illawarra region.
Damaging winds, large hailstones and heavy rainfall that may lead to flash flooding were considered likely.
Residents were warned to move their cars under cover and away from trees, secure any loose items around the house or yard, and keep at least eight metres from any fallen power lines.
Melbourne is also in the midst of severe weather warnings.
Shortly after 4pm, the BoM warned residents a severe thunderstorm system had formed in central Victoria and the state’s south, bringing heavy rain to the region.
“(Severe thunderstorms) are forecast to affect Altona, Footscray, Lara and Laverton by 4:40 pm and Melbourne City, St Kilda, Toorak and Williamstown by 5:10pm,” it said in a statement.
“Heavy rainfall that may lead to flash flooding is likely.”
It comes as floods continue in parts of the state.
Since rainfall data collection began in 1858, meteorologists from Weatherzone said they’ve never seen weather conditions “even come close” to 2022 levels.
Local wildlife left stranded by rising floodwaters
The previous 1987 record of 285mm was superseded today when Sydney’s running monthly total reached 286.8mm at 10.40am.