"An anti-terrorism operation led to the arrest of three women linked to an abandoned car containing gas cylinders on Thursday," Xinhua news agency quoted Cazeneuve as saying.
The suspects aged 19, 23 and 39 were "likely preparing a violent and imminent action", he said.
A police officer was injured on the shoulder when one of the women attacked him with a knife in the southeast of Paris, the minister said.
The 19-year-old woman is known to the police for attempting to leave for Syria.
The car owner, who is on the intelligence services watchlist for radicalisation, was taken into custody earlier this week but later released due to lack of evidence.
He had gone to police on Sunday to report that his daughter had disappeared with his car, officials said.
A bar employee working near Notre Dame had first raised an alarm on Sunday after noticing a gas cylinder in the back seat of a grey Peugeot 607, the police said.
The car, with no registration plates, contained seven gas cylinders, including an empty one on the passenger seat and three cans of diesel fuel. It was found parked in a no-parking area with its hazard lights flashing.
"It may have been that they were on a test run," said a source close to the case.
"There was nobody in the car, and the cannisters were not connected to any detonator or explosives. Documents written in Arabic were also found in the car," The Daily Mail quoted the source as saying.
Florence Berthout, mayor of Paris's Fifth Arrondissement, said the incident had highlighted the need to beef up security and put more police on patrol in one of the world's most visited cities.
This comes after four people -- two brothers and their girlfriends -- were arrested for links with radical Islamists.
The first couple, a 34-year-old man and a 29-year-old woman, were arrested on a motorway in southern France and are known to the security services for links to radical Islamists. The man's brother and his girlfriend, both aged 26, were arrested late Wednesday.
At least 84 people were killed and more than 250 injured when a heavy duty white truck ploughed into a crowd celebrating Bastille Day on July 14 in the southern city of Nice.
On July 26, two young men took six hostages in a church in northern France, killed a priest and seriously wounded another. They were shot dead by the police. The Islamic State militant group claimed responsibility for the attack.
A state of emergency has been imposed in France after at least 130 people were killed and over 350 injured when IS militants attacked multiple places in Paris on November 13 last year.
