The man, aged in his late 30s, was intercepted on a motorway north of Paris in the vehicle used to drive into the soldiers, the sources added.
One source close to the case said the man had been stopped at the wheel of a BMW driving towards Calais.
A second source added: “The arrested individual, born in 1980, is suspected to be the culprit” of the attack in the Levallois-Perret around 8:00 am.
“He was driving the vehicle we were looking for and tried to flee,” the source added, leading police to open fire.
Six soldiers were injured after a car slammed into soldiers on patrol on Wednesday morning.
Earlier, the mayor of Levallois-Peret, Patrick Balkany, described the incident “a deliberate act”, while French Interior Minister Gerard Collomb said the deliberate act was carried out by a "man on his own".
French Defence Minister Florence Parly condemned the incident as a “cowardly act”. The incident “does nothing to dent soldiers’ determination to work for the security of the French people,” she said in a statement.
The Paris prosecutors’ office said its anti-terrorism unit has launched a probe into “attempted killings... in relation to a terrorist undertaking”.
The soldiers are part of the 7,000-strong anti-terrorism ‘Sentinelle’ force set up in January 2015 which sees armed, uniformed soldiers patrol the streets and guard high-risk areas such as tourist sites and religious buildings.
France has been under a state of emergency since November 2015 and has seen a string of attacks on security forces, particularly those guarding key tourist sites.
An 18-year-old with a history of psychological problems was arrested on Saturday at the Eiffel Tower after brandishing a knife and shouting “Allahu Akbar” (God is Greatest).
He told investigators he wanted to kill a soldier, sources told the news agency AFP.
In February, a man armed with a machete attacked four soldiers on patrol at Paris's Louvre Museum, while in April another extremist shot and killed a policeman on the Champs Elysees.
In June, a 40-year-old Algeria doctorate student who had pledged allegiance to the Islamic State group attacked a policeman with a hammer outside the Notre Dame cathedral.
- with AFP