The soldier was patrolling with two other soldiers in the business district of Paris on Saturday when someone approached him from behind and stabbed him with a knife or a box-cutter.
The assailant quickly fled the scene after the attack, which occurred at 6:00 p.m. local time.
Later in the day, French president Francois Hollande took time out during his trip to the African Union summit in Addis Ababa, Ethiopia to comment on the incident, saying that the man is on the run and the police are conducting an investigation.
"We still do not know the exact circumstances of the attack or the identity of the attacker, but we are exploring all options," the French president said.
On May 22, Lee Rigby, a 25-year-old British soldier, was run over by a car in London and then stabbed to death.
"At this stage no link was established with the murder of the British soldier. But, we must study all the assumptions," Hollande said.
French Interior Minister Manuel Valls noted the similarity between the two attacks, saying the assailant meant to kill his victim.
"Let's be prudent for now… Everything is being done to arrest this individual," the French interior minister said.
The soldier, who was from the 4th Regiment of Gap Chasseurs, was patrolling as part of the Vigipirate anti-terrorist plan.