Contact was lost about 50 minutes after take-off from Ouagadougou, it said. The plane was last seen at 01:55 GMT.
Air Algerie said 50 French citizens were among the 110 passengers and six crew on board Flight AH 5017.
The pilot had contacted Niger’s control tower in Niamey to change course because of a storm, correspondents say.
BBC West Africa correspondent Thomas Fessy says the route is well used by French travelers.
France’s civil aviation body said crisis centers had been set up at airports in Paris and Marseille.
An Air Algerie spokesman quoted by Reuters said the provisional passenger list also included 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.
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.
The plane is operated by Air Algerie and chartered from Swiftair.
Algerian Prime Minister Abdelmalek Sellal reportedly told Algerian radio: “The plane disappeared at Gao (in Mali), 500 kilometers (300 miles) from the Algerian border.”
U.N. 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 U.N. 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, the correspondent adds.