She is said to have been wounded when a police officer opened fire after the suspect stabbed another officer during the arrest.
His injuries are said to not be life-threatening.
The woman was detained in Boussy-Saint-Antoine on the outskirts of Paris, and is said to be one of the daughters of the owner of the vehicle
Two other women have also been held in the anti-terror operation.
The French Interior Minister said all three were likely to be planning an “imminent violent attack”.
Bernard Cazeneuve said the detentions of the “radicalised” women aged 19, 23, and 39 are linked to the discovery of an abandoned Peugeot 607 on a Seine riverside road on Sunday.
Police said it was loaded with seven gas canisters, six of them full, and also three jerrycans of diesel.
Documents with writing in Arabic were also found in the car, which had no registration plates and was left with its hazard lights flashing.
Officers said there were no detonator devices found in the car, but the contents of the cylinders suggested there could have been a plan to explode the vehicle.
The car owner had been taken into custody earlier this week but was later released.
He had gone to police on Sunday to report that his daughter had disappeared with his car.
His daughter is known to police for wanting to leave for Syria, officials said.
Four other people suspected of being “radical Islamists” have also been arrested in the same case.
Officials said a 27-year-old man and a woman, 26, were held south of Paris on Wednesday, and a second couple – a 34-year-old man and a woman, aged 29 – were detained on a motorway in southern France on Tuesday.
Meanwhile, prosecutors in Austria have charged two men with being part of Islamic State as part of ongoing investigations into the Paris attacks.
The 26-year-old Moroccan and 40-year-old Algerian, who were arrested on 18 December, are suspected of helping two other suspects extradited to France earlier this year.
Salah Abdeslam, who is accused of playing a key role in the terror plot, kept silent during a court hearing in Paris on Thursday.
The 26-year-old refused to attend a similar hearing in July.
His lawyer said his silence was linked to 24-hour surveillance in his cell.
France remains on maximum alert after more than 230 people died in terror incidents in the past 18 months.
News Source SkyNews