Detectives are also examining whether there is a link between the attack and the killing of a British soldier who was hacked to death in London on Wednesday.
The 23-year-old French soldier, Pfc. Cedric Cordier, was patrolling the busy underground corridors beneath the La Defense arch in the French capital's business district with two other soldiers when an attacker approached him from behind shortly before 6 p.m. on Saturday, authorities said. They said Cordier was stabbed in the neck with a knife or cutter that narrowly missed his carotid artery.
The soldier, a member of the Gap 4th Rifle Regiment, was taken to a hospital, where doctors said his life was not in danger. The attacker, who fled into a nearby shopping center, was described as of North African appearance and around 30 years old. He was still being sought on Sunday.
The area where the attack occurred adjoins the busy La Defense train station, and is monitored by video cameras run by the city transport network. Investigators are now going through footage from the cameras.
French Defense Minister Jean-Yves Le Drian, who visited Cordier in the hospital a few hours after Saturday's attack, said it was clear the victim was targeted because he was a soldier. Le Drian and Interior Minister Manuel Valls issued a joint statement condemning what they described as a "cowardly attack" on the soldier.
On Sunday, Valls told France 5 television there were "elements" that led police to believe it was a terrorist act.
"I cannot say more at this stage as the inquiry has only just begun," he said.
President François Hollande, on an official visit to Ethiopia, said "all hypotheses" would be investigated.
"At this stage, I don't think there's a link [with the London attack], but we're asking all our soldiers to be even more aware and vigilant," Hollande said.
France has been on heightened security alert since the country launched a military intervention in Mali in January to drive out Islamic fundamentalists who had been pushing through the country from the north.
The Paris stabbing came just three days after two men attacked British soldier Lee Rigby in the London neighborhood of Woolwich. Rigby, 22, was first run down by a car before the men jumped from the vehicle and attacked him with a knife and meat cleaver.
The London attackers were said to have cried "Allah Akbar" (God is great) as they attacked Rigby, leading to suggestions they were part of an Islamic extremist group. The men were later shot by police and are now under hospital arrest.
Christophe Crepin, a spokesman for the French police union, said there were similarities between the attacks. "I think this person wanted to imitate what happened in London," he told French television.