The soldier was patrolling a business area of western Paris as part of France's 'Vigipirate' anti-terrorist surveillance plan.
A police source told French newspaper Le Parisien that the soldier was stabbed in the early hours of Saturday evening, at around 6pm.
The source said the soldier was expected to survive the attack.
The attacker, who the source said was a bearded man of North African origin, fled the scene.
Police are searching for the suspect, said to be around 30 years old, wearing an Arab-style garment under his jacket.
The stabbing comes just a few days after the murder of British soldier Lee Rigby, who was killed on Wednesday, raising fears it may be a copycat killing.