The suspect, known as a radical Muslim, was detained on Wednesday morning in the Yvelines region, 45 km (28 miles) southwest of the capital, Interior Minister Manuel Valls said.
The “dangerous” man was traced thanks to evidence at the scene, he added.
French anti-terrorist investigators are handling the case, saying the soldier was targeted because of his profession.
Witnesses had earlier described the attacker as a bearded man of North African origin.
The man, named Alexandre, was monitored on security cameras and seen taking off his robe and running away wearing European clothes, officials said.
The stabbing took place three days after the killing of British serviceman Drummer Lee Rigby outside a barracks in the Woolwich area of London.
French President Francois Hollande said that while all theories would be investigated, there was no evidence to link the two attacks.
The suspect was a petty criminal known to police, correspondents say.
Speaking on French TV on Wednesday, Manuel Walls warned against jumping to early conclusions.
The minister said that although there were signs that the suspect may be linked to radical Islam, the investigation was still in its early stages.
“I remain cautious,” the minister said.
“We need to know more about his motives, his background, his family environment.”
Pfc Cedric Cordier, 23, was approached from behind and stabbed in the neck with a small-bladed knife in La Defense business district on Saturday.
The attack took place in a busy underground hall where shops and public transport lines converge in La Defense business district.
The victim was in a stable condition after the attack, police said.
France is on high alert following a threat from the North African wing of al-Qaeda, related to the country’s involvement in Mali.
The raised alert level is one of the reasons why soldiers are on patrol in central Paris and other high-profile areas, correspondents say.
Last March, soldiers were targeted by Islamist militant Mohamed Merah in the Toulouse area of southern France.
He shot dead three French paratroopers then attacked a Jewish school, murdering three children and an adult, before being killed in a police siege.
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