The attack occurred on Saturday night near the central train station in Strasbourg, reported BFM TV.
At around 8pm, the man was reportedly walking in the same direction as some patrol troops when he turned around, sliced the face of one of the soldiers, then fled the scene.
The soldiers, who were patrolling the station as part of France's heightened security measures following last year's terror attacks, allowed the man to escape rather than risking the safety of the public or causing a stampede, they said.
The aggressor was reportedly speaking Arabic at the time, though did not say "Allahu Akbar" (God is greatest) as has been the case in previous random attacks on soldiers and police in France.
The soldier did not sustain serious injuries, the channel reported.
Ever since the terror attacks in Paris last January, France has seen armed soldiers patrolling the streets, especially in busy areas like train stations and tourist attractions.
Since then there have incidents where soldiers have been attacked, by individuals.
In February last year, a man attacked three soldiers with a knife in southern France's Nice. Two of the troops received wounds.
In January this year, a man was shot and wounded after driving his car at four soldiers guarding a mosque in southeastern France.
In May 2013 a solder was attacked by a man with a knife in La Defense business district near Paris.
The incidents were blamed on individuals with mental health problems rather than terror attacks.
Nevertheless soldiers and police officers, who have also been targeted by individuals in the street, remain on high alert.