The vehicle accelerated into the soldiers when they were just a few metres away, Interior Minister Gerard Collomb told reporters outside the hospital where the three more seriously injured victims were being treated.
Counter-terrorism prosecutors opened an investigation on potential charges of attempted murder of security forces in connection with a terrorist enterprise, the Paris prosecutor's office said.
He was lurking as two three-man patrols swapped shifts, and then he approached them slowly "before speeding up", said Mr Balkany.
The mayor of Levallois-Perret, Patrick Balkany, said the auto had already taken off in a small alley, waiting for troops from the 35th Infantry Regiment to get out of the building.
As reported by CBS News, six soldiers were injured in the incident, with two receiving serious injuries, when the driver of a BMW vehicle drove into them at 8 a.m. local time this morning.
10,000 soldiers are now patrolling France as part of the operation.
Levallois-Perret is about 5 kilometres (3 miles) from city centre landmarks such as the Eiffel Tower and the Elysee Presidential Palace and is the site of the latest attack targeting security forces in France.
Most recently, in June, an Islamic State supporter drove a auto carrying firearms and a gas canister into a military vehicle stationed on the Champs Élysées in central Paris, but luckily nobody other than the driver was hurt.
The army group is part of the French Sentinel Operation, formed after Charlie Hebdo's terror attack in January 2015.
Judiciary police start to investigate near the site where six soldiers of the anti-terrorism Sentinelle Operation were hit by a auto in Levallois-Perret, near Paris, France, 09 August 2017.
French police arrest a man suspected of an intentional hit-and-run attack which left six anti-terror soldiers injured. Two officers sustained serious injuries and the rest suffered moderate ones in the Wednesday morning attack.
The soldiers, which belong to the the 35th infantry regiment, were hospitalized at the Bégin military hospital in Saint-Mandé, in Paris' eastern suburbs. This morning, a vehicle attacked a group of officers, who were in the vicinity of a building of the government of Levallois-Perret, on the outskirts of Paris.
"It's an odious act of aggression..."
"It was a BMW which accelerated very quickly the moment they came out".
Witnesses said the auto was parked, apparently in wait, on a small road not far from the Town Hall. The soldiers were rushed to the hospital, he added.
The Islamic State in Iraq and Syria (ISIS) group has repeatedly targeted France because of its participation in the US-led worldwide coalition fighting the Islamist militants, with French jets carrying out air strikes in Syria.
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