Flight AH 5017, chartered from Spanish airline Swiftair, was carrying 110 passengers and six crew, it said.
French Foreign Minister Laurent Fabius said the plane, which has 50 French citizens aboard, “probably crashed”.
Contact was lost about 50 minutes after take-off from Ouagadougou, Air Algerie said, as the plane crossed Mali.
The pilot had contacted Niger’s control tower in Niamey to change course because of a storm, officials say.
BBC West Africa correspondent Thomas Fessy says the route is well used by French travellers.
Speaking in Paris, Mr Fabius said French Mirage fighter planes were scouring the area for the aircraft.
“Despite intensive search efforts no trace of the aircraft has yet been found,” he said.
“The plane probably crashed.”
Earlier, an Algerian official told Reuters that the plane had crashed, but gave no further details.
France’s civil aviation body said crisis centres had been set up at airports in Paris and Marseille.
An Air Algerie spokesman quoted by Reuters said the provisional passenger list included 50 French citizens, 24 people from Burkina Faso, eight Lebanese, four Algerians, two from Luxembourg, one Belgian, one Swiss, one Nigerian, one Cameroonian, one Ukrainian and one Romanian.
The six crew members are Spanish, according to the Spanish pilots’ union.
Officials in Lebanon, however, said there were at least 10 Lebanese citizens on the flight.
“In keeping with procedures, Air Algerie has launched its emergency plan,” Air Algerie officials, quoted by APS news agency (in French), said.
Algerian Prime Minister Abdelmalek Sellal reportedly told Algerian radio: “The plane disappeared at Gao (in Mali), 500km (300 miles) from the Algerian border.”
Burkina Faso Transport Minister Jean Bertin Ouedraogo said the plane sent its last message at around 01:30 GMT, asking air traffic controllers in Niger to change its route because of heavy rain.
UN troops in Mali say they understand the plane came down between Gao and Tessalit, the BBC’s Alex Duval Smith in the Malian capital Bamako reports.
Brigadier General Koko Essien, who is leading the UN troops, told the BBC that the area leading up to the Algerian border was vast and sparsely populated.
He added that weather in the area had been bad overnight.
Armed groups are also said to be active in the area. However, at the moment the most probable scenario looks like a plane that came down in bad weather, our correspondent adds.
Swiftair said that the aircraft was an MD83 and that they were unable to establish contact with it.
An Algerian official had previously told Reuters that the plane was an Airbus A320.
An unnamed Air Algerie company source, speaking to AFP news agency, said: “The plane was not far from the Algerian frontier when the crew was asked to make a detour because of poor visibility and to prevent the risk of collision with another aircraft on the Algiers-Bamako route.”
“Contact was lost after the change of course.”
Flight AH 5017 flies the Ouagadougou-Algiers route four times a week, AFP reported.
French Transport Minister Frederic Cuvillier told reporters that it was likely there were also many French nationals on board the plane.
In February a military plane in Algeria crashed, killing 77 people on board.
The Hercules C-130 crashed into a mountain in Oum al-Bouaghi province, en route to Constantine, in bad weather conditions. Only one person on board survived.
Twin rear-engine, short-medium range airliner
More powerful version of the MD-80 type, based on earlier DC-9
Range: 4,637km (2,881 miles)
Capacity: 172 passengers
First flew: 1984