"A terrorist cell made up of young women totally receptive to the deadly ideology of Daesh has been dismantled," Francois Molins said in a press conference, using the Arabic name for IS.
The three women, led by 19-year-old Ines Madani, were arrested south of Paris yesterday.
They were "determined" to launch an attack, Molins said.
A car laden with gas cylinders found abandoned near Notre Dame cathedral in Paris on Sunday belonged to Madani's father and the keys were found in her possession.
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Investigators have learned that one of the women arrested was the fiancee of Larossi Abballa, who killed a senior police officer and his partner at their home in a Paris suburb in June before himself being shot dead, Molins said.
The woman, identified only as Sarah H., then became engaged to Adel Kermiche, one of two jihadists who slit the throat of an elderly priest in July near the northern city of Rouen, the prosecutor said.
The developments came after the owner of the abandoned car was identified by the insurance badge that remained on the car's windscreen even though the number plates had been removed.
Madani was already known to intelligence services after trying several times to travel to Syria, the prosecutor said.
She had sworn allegiance to IS in a letter found in her handbag.
Today, the woman identified as Sarah H., 23, stabbed a policeman in the shoulder who had been keeping watch on them from an unmarked car near the apartment, the investigator said.
Teams of police then swooped on the women and in the struggle, Madani was shot in the thigh and the ankle.
The prosecutor said there was evidence that attempts had been made to light the gas cylinders found in the car near Notre Dame in the heart of Paris' tourist district.
"A half-smoked cigarette" and a piece of material soaked in flammable liquid found in the boot of the car had been used to try to light one of the gas cylinders.