The attacker fled the scene after stabbing 23-year-old Cedric Cordier on Saturday afternoon in La Defense business district, which at weekends is packed with shoppers.
The local prosecutor's office said anti-terror investigators would handle the probe into the attack, which was captured by surveillance cameras.
The soldier, who was armed and in uniform, was patrolling as part of France's Vigipirate anti-terrorist surveillance scheme that sees troops deployed at high-profile tourist, business and transport sites across the capital
The attacker, described by police as around 1.9 meters (six foot three inches) tall, bearded and wearing a jersey and black trousers, approached his victim, stabbed him and then melted into the crowd without saying a word.
The soldier was with two colleagues on patrol in a busy underground space that hosts shops and provides access to several underground train lines.
Hollande told reporters accompanying him on a trip to Ethiopia: "We still do not know the exact circumstances of the attack or the identity of the attacker, but we are looking at all options."
"I do not think that at this stage a link can be made" to the attack in London on Wednesday, he said.
That assault saw a soldier hacked to death on a London street by two men wielding knives and a cleaver who then launched into a tirade against British military involvement in Muslim countries.
Defence Minister Jean-Yves Le Drian visited the wounded man in hospital and later told reporters he had been targeted because he was a soldier.
Le Drian, who said the soldier was in a stable condition, vowed to continue France's "implacable" fight against terrorism.
Police sources said the victim would survive the attack but gave no indication of the possible motive for the assault.
Prosecutor Robert Gelli said the attacker struck the soldier from behind with a sharp metal object, but he did not confirm earlier reports that the weapon used was a box cutter.
In March last year, self-declared Islamist Mohamed Merah killed seven people in a shooting spree in and around the city of Toulouse. Three of them were French soldiers.
Hollande earlier this month said France was taking seriously a call by Al-Qaeda's North African wing for Muslims worldwide to launch attacks against the country's interests over its military operation in Mali, where French soldiers this year intervened to fight Islamist extremists.
Interior Minister Manuel Valls said Saturday that "there were elements, such as the sudden violence of the attack (on the soldier in Paris), that could lead one to think there is a form of comparison with what happened in London".
But he said in a television interview that investigators must be cautious and could not yet draw such conclusions, while adding that the attacker had clearly intended to kill the soldier.
In London, three more men were arrested on Saturday on suspicion of conspiracy to murder the soldier, who was hacked to death in the street in broad daylight.