The second largest airport in the French capital was evacuated following the shooting at around 8:30am (0730GMT) and both terminals were closed, airport authorities said.
“A man took a weapon from a soldier then hid in a shop in the airport before being shot dead by security forces,” interior ministry spokesman Pierre-Henry Brandet told AFP.
He said no one was wounded in the incident. Interior Minister Bruno Le Roux is due to visit the facility, in Paris’ southern outskirts.
Brandet said de-mining operations were underway to determine if the man had explosives on him. He said nearly 3,000 people had been evacuated from the southern terminal alone but those in the other one had been “confined”.
Traffic to Orly has been "completely suspended," France's civil aviation authority said.
France is still in a state of emergency after a series of terror attacks, including the November 2015 massacre in Paris and a truck attack in Nice, in July last year. In mid-February, an Egyptian staged a machete attack in Paris's Louvre museum before being shot and wounded.
The latest shooting comes weeks ahead of the first round of France's two-stage presidential election, in which security is one of the main issues on voters' minds.
“We had queued up to check in for the Tel Aviv flight when we heard three or four shots nearby,” witness Franck Lecam said.
“We are all outside the airport, about 200 metres from the entrance,” the 54-year-old Lecam said.
“There are policemen, emergency workers and soldiers everywhere in all directions. A security official told us that it happened near gates 37-38 where Turkish Airlines flights were scheduled.”
The soldier from whom the man took the weapon was a part of Operation Sentinelle, deployed after the January 2015 Paris attacks.
It involves some 7,000 troops of whom roughly half are deployed in the Paris region. They are charged with guarding religious sites which could be targets of terror attacks as well as airports, railway stations and tourist spots.
A notice was posted on the Paris airports authority website urging passengers not to travel to Orly.
Budget airlines easyJet said in a statement that “like all other airlines” it expected interruptions and flight delays, adding that 46 of its flights were due to fly in and out of the airport on Saturday.
On Thursday, a letter bomb exploded at the Paris offices of the International Monetary Fund, injuring a secretary who suffered burns to her hands and face.
French President Francois Hollande called it an “attack”, saying it showed the country was “still targeted”.
“All this leads me to justify the state of emergency” that has been in effect since November 2015, Hollande said.
The Paris letter bomb coincided with a school shooting in the southern town of Grasse that left around 10 people injured and rattled nerves.