The company said in a notice posted on its website that the aircraft took off from Burkina Faso at 0117 local time and was supposed to land in Algiers at 0510 local time but never reached its destination.
Its six-member crew were all Spanish, said Spain's airline pilots' union Sepla, while Swiftair confirmed the aircraft had gone missing less than an hour after takeoff from Ouagadougou.
Many French nationals were thought to be on board the plane, France's Transport Minister Frederic Cuvillier said in Paris.
He said after a government meeting that top civil aviation officials were holding an emergency meeting and a crisis cell had been set up.
"The plane disappeared at Gao (in Mali), 500 kilometers (300 miles) from the Algerian border. Several nationalities are among the victims," Prime Minister Abdelmalek Sellal was cited as saying by Algerian radio.
Despite international military intervention still under way, the situation remains unstable in northern Mali, which was seized by jihadist groups for several months in 2012.
On July 17, the Bamako government and armed groups from northern Mali launched tough talks in Algiers aimed at securing an elusive peace deal, and with parts of the country still mired in conflict.