"We have found the Algerian plane. The wreck has been located ... 50 kilometres north of the Burkina Faso border" in the Malian region of Gossi, said General Gilbert Diendiere of the Burkina Faso army.
"At the moment we have no further information on (the fate of) the passengers but our teams are hard at work," he said.
Diendiere gave no indication as to what may have caused the plane to crash.
A witness had earlier reported seeing the plane "falling" in the Gossi region.
Flight AH5017, which took off from Ouagadougou bound for Algiers with 51 French nationals aboard, according to Foreign Minister Laurent Fabius, went missing amid reports of heavy storms, company sources and officials said.
The airline said there were also 24 Burkinabe, eight Lebanese, six Algerians, six Spanish, five Canadians, four Germans and two Luxembourg nationals on board.
The flight had been presumed lost even before French President Francois Hollande appeared on TV to announce: "Everything leads us to believe that the plane has crashed."
He said the plane's Spanish crew had signalled they were altering course "due to particularly difficult weather conditions".
"Contact was lost with the McDonnell Douglas 83 at 1.47 (local time), a little after the pilots said they were diverting from the route due to meteorological reasons," Fabius said earlier.
Algerian radio quoted Prime Minister Abdelmalek Sellal as saying the plane dropped off the radar at Gao, 500 kilometres from the Algerian border.
- Poor visibility -
Mali, Algeria, Niger and France coordinated their search efforts under the umbrella of the French-led military intervention in Mali, Operation Serval.
"Even though the aircraft was above Mali it was in airspace managed by the control centre in Niamey in Niger," an air traffic control official told AFP.
Aviation sources told AFP the MD-83 was leased from Spanish company Swiftair.
Its six-member crew were all Spanish, said Spain's airline pilots' union Sepla, and Swiftair confirmed the aircraft went missing less than an hour after take-off.
"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," an airline source said.
"Contact was lost after the change of course."
The plane had apparently been given the "all clear" following an inspection in France only this week, French civil aviation authority DGAC said.
In France, two crisis units were set up, one at the DGAC and another at the foreign ministry, in addition to two further centres at Charles De Gaulle airport in Paris and at Marseille airport.
DGAC said many passengers had been due to catch onward connecting flights to Paris and Marseille.
France's minister responsible for French abroad, Fleur Pellerin, was due in Ouagadougou later Thursday.
One French family had seven people on the plane, a brother of one passenger told AFP.
"There was my brother, his wife and their four children, plus my nephew," Amadou Ouedraogo said via telephone.
- 'Emergency plan' -
A controller in Mali, speaking on condition of anonymity, said the area was rocked by "strong storms" overnight.
Air Algerie, in a statement carried by national news agency APS, said it had initiated an "emergency plan" in the search for AH5017, which flies the four-hour passenger route four times a week.
In Cuba, the daughter of President Raul Castro assured journalists she was alive and well, contradicting reports that she had been onboard the doomed flight.
Mariela Castro, a sexologist and gay rights activist, said she had been told there was another passenger of the same name aboard flight AH5017.
The crash comes at the end of a disastrous week for the aviation industry.
On July 17, a Malaysia Airlines plane crashed in eastern Ukraine, killing all 298 people on board.
A Taiwanese aircraft crashed in torrential rain in southwest Taiwan on Wednesday, killing 48.
In February, a C-130 military aircraft carrying 78 people in Algeria's mountainous northeast crashed, killing more than 70 people.
The plane had been flying from the desert garrison town of Tamanrasset in Algeria's deep south to Constantine, 320 kilometres east of Algiers.
Tamanrasset was also the site of the country's worst-ever civilian air disaster, in March 2003 that killed all but one of the 103 people onboard an Air Algerie Boeing 737-200.