The soldier, who was part of an anti-terrorism operation known as Sentinelle, rapidly tackled the man and was uninjured. The attacker was taken into custody.
The man had lunged at the soldier at the central Chatelet metro station around 6.30 am (0430 GMT), making reference to Allah, a police source said. The attacker was not previously known to police.
Investigators have opened an anti-terror probe, government spokesman Christophe Castaner said.
The incident came with France still on high alert following a string of terror attacks which began in January 2015 when jihadist gunmen stormed the offices of satirical weekly Charlie Hebdo, killing 12.
Since then the troops have been attacked seven times, including last month when a man rammed a car into a group of soldiers in the Paris suburbs, injuring six.
Though much smaller in scale than the 2014 Islamic State attacks in Paris and last year's truck attack in Nice, the repeated assaults on soldiers have sparked criticism that their patrols have become a target.
But defence minister Florence Parly said the fact that the attacker was swiftly brought under control Friday was "proof of the professionalism and efficiency of the Sentinelle soldiers in their mission to protect".
In February, a 29-year-old Egyptian brandishing machetes in each hand attacked four soldiers patrolling near the Louvre museum in Paris, shouting "Allahu akbar" (God is greatest).
In March, a man was shot dead at the capital's Orly airport after attacking troops.
Today's attack came a day after Interior Minister Gerard Collomb said the Sentinelle operation would "evolve" but ruled out cuts to troop numbers.
"We want to redeploy it to do better against the threat we are facing today," Collomb said, adding there would be changes to the way the force is organised.
Critics argue that the patrols have done little to increase security and that troops are placed at unnecessary risk for an operation largely aimed at reassuring the public.
They also point to the strain it puts on an army that has 10,000 troops active abroad, including 4,000 fighting jihadism in west Africa.
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