There were few clear indications of what might have happened to flight AH5017, or whether there were casualties, but Burkina Faso's transport minister said the crew asked to adjust their route at 0138 GMT because of a storm in the area.
"I can confirm that it has crashed," the Algerian official told Reuters, declining to be identified or give any details about what had happened to the aircraft on its way north.
French Foreign Minister Laurent Fabius said the Air Algerie flight was still missing, but had probably crashed.
"Despite intensive search efforts no trace of the aircraft has yet been found," Fabius told journalists in Paris. "The plane probably crashed."
French President Francois Hollande cancelled a planned visit to overseas territories and said all military means on the ground would be used to locate the aircraft.
Two French Mirage warplanes have been scouring the vast desert area around the northern Malian city of Gao for the aircraft, which had 51 French nationals on board.
"The search will take as long as needed," Hollande told reporters. "Everything must be done to find this plane. We cannot identify the causes of what happened," he said.
Niger security sources said planes were flying over the border region with Mali to search for the flight.
The Malian government, which is holding talks with the separatists in neighbouring Algeria, has only a weak presence in the region and relies on French and UN peacekeepers for aircraft and logistical support.
Whatever the cause, another plane crash is likely to add to nerves over flying after a Malaysia Airlines plane was downed over Ukraine last week, a TransAsia Airways crashed off Taiwan during a thunderstorm on Wednesday and airlines temporarily cancelled flights into Tel Aviv due to the conflict in Gaza.
French passengers
Algeria's state news agency APS said authorities lost contact with flight an hour after it took off from Burkina Faso, but other officials gave differing accounts of the times of contact, adding to confusion about the plane's fate.
A total of 265 of the MD-83 model were delivered before McDonnell Douglas, by then part of Boeing, halted production in 1999.
"Boeing is aware of the report. We are awaiting additional information," a spokesman for the US planemaker said.
According to the Ascend Fleets database held by British-based Flightglobal, there are 187 MD-83s still in operation, of which 80 percent are being flown in the United States.
The aircraft's two engines are made by Pratt & Whitney, a unit of United Technologies.
Swiftair has a relatively clean safety record, with five accidents since 1977, two of which caused a total of eight deaths, according to the Washington-based Flight Safety Foundation.
Air Algerie's last major accident was in 2003 when one of its planes crashed shortly after take-off from the southern city of Tamanrasset, killing 102 people.
In February this year, 77 people died when an Algerian military transport plane crashed into a mountain in eastern Algeria.