Sky News reported the 23-year-old victim was with two other soldiers when his assailant approached from behind in a busy underground train station about 6 p.m., cut him with a knife or box-cutter and fled.
Sky News said CCTV footage showed the assailant was a tall, bearded man, about 35 years old, possibly of North African origin and wearing a white Arab-style tunic.
"They tried to kill the soldier because he was a soldier," Defense Minister Jean-Yves Le Drian said.
Le Drian said the soldier, whose name was not released, was in stable condition.
French President Francois Hollande said authorities were investigating all possibilities, including whether the attack was linked to the fatal machete attack in London this week on British soldier Drummer Lee Rigby.
"There could be a link, but we will look at all the elements," Holland said.
The BBC noted France is on high alert after a threat from the North African wing of al-Qaida concerning the country's involvement in putting down an insurgency in Mali. Soldiers are patrolling in central Paris as part of the tightened security.