None of the soldiers were wounded, Paris Prosecutor Francois Molins said. The suspect, identified by Molins as Ziyed Ben Belgacem also is accused of shooting a police officer earlier in the day when he stole the officer's weapon. That officer has non-life-threatening wounds, officials said.
Molins said the suspect had been imprisoned several times on violence and theft convictions, including one five-year stint that began in 2009.
French terrorism investigators will lead the inquiry into the attacks, Molins said.
When Belgacem got to Orly Airport in the southern outskirts of Paris, he went to the South Terminal, carrying a weapon and a can of gas in his rucksack, Molins said.
He grabbed the female soldier and used her as a shield. They struggled over her weapon, the prosecutor said. With the soldier down on her knees, the suspect rose enough for the other two soldiers to shoot him several times. The whole scene unfolded in just a couple of minutes, Molins said.
Three relatives of the suspect were later taken into custody, Molins said. Belgacem's plans are unclear, he said, adding that an investigation will determine whether he acted as a "lone wolf."
Prior attack on Saturday
Molins said Belgacem was involved in several incidents before heading to the airport.
• 6:55 a.m.: Shoots police officer after being stopped for speeding and driving with headlights turned off near Stains, in northern suburbs of Paris.
• Time not given: Goes to a bar in Vitry-sur-Seine where he had been until 3 a.m. and fires four shots with gun stolen from police officer. No one is wounded.
• Short time later: Drives from bar (where he leaves cell phone), carjacks a new vehicle
8:06 a.m. -- Arrives at Orly airport
About 16 minutes later, Belgacem assaulted the soldier.
Hours after the airport incident, police launched an operation in the same northern Paris suburb where the officer was shot, the National Police tweeted. The agency did not specify the reason for the operation.
Police were questioning Belgacem's father and brother, Thibault-Lecuivre said. The attacker, who was born in 1978, was under supervision by authorities, Molins said, echoing Interior Minister Bruno Le Roux's earlier comments that Belgacem was known to intelligence services.
Soldiers lauded for response
French Defense Minister Jean-Yves Le Drian commended the soldiers who responded to the airport threat.
They responded with "remarkable professionalism and self-control" to protect their colleague and the public, he said.
This was the fourth attack against security forces deployed as part of France's Operation Sentinel, Le Drian said. The national security operation was launched following the Paris terror attacks in January 2015; France has been under a state of emergency since November that year.
Le Roux also praised the swift response of security forces at the airport.
President François Hollande said the incident demonstrated that the ongoing national security operation -- which has placed extra security forces at airports, train stations and other public places -- is "absolutely essential" to keep people safe.
"I want to salute the courage and the exceptional behavior of the security forces who managed to put away the individual and to do so in an extremely complex situation because this occurred in Orly Airport," he said at a news conference.
The anti-terrorism prosecutor is investigating the motives and circumstances of Saturday's attack and the existence of any accomplices, according to a presidential statement.
Politicians add praise
France's presidential candidates, who are campaigning ahead of next month's first round of voting, took to Twitter to pay tribute to the response by the police and the military.
Emmanuel Macron, an independent centrist, said the military "once again showed their professionalism this morning in Orly."
François Fillon, of the centre-right Republican party, said: "Tribute to the men and women of Sentinel who work for our security and once again displayed courage and efficiency."
Marine Le Pen, presidential candidate for the far-right Front National party, said: "France brimming over with violence, a consequence of the lax successive governments. But there is the bravery of our soldiers!"
Bomb squad called in
The airport was evacuated as an elite operations unit and bomb squad officers rushed to the scene. The bomb squad finished its search for explosives but did not immediately report the findings, local authorities said. More than 450 officers were involved in the operation to secure the airport and search for evidence, France's National Police said.
Paris Airports, the group that manages the city's airports, said both Orly terminals were reopening Saturday afternoon after a suspension of several hours. Travelers should check with their airlines before heading to the airport, it added. Some earlier flights were rerouted to Paris Charles De Gaulle Airport.
Travel for about 2,000 people had been severely disrupted, the president of Paris Airports, Augustin de Romanet, told CNN.
"It has been very disruptive, because we could fear many, many things, but all the police forces and the army have been very effective, so everything is OK now," he said.
With roads around the airport closed off by police as the security operation unfolded, travelers earlier tried to make their way to the airport on foot with their baggage.
Paris Orly Airport is France's second-busiest airport, with international and domestic air traffic.