According to reports, three female survivors have been rushed to hospital and are in a critical condition after emergency services freed them from the wreckage.
The Boeing 737 operated by Cuban airline Cubana de Aviacion is thought to have had 110 people on board, including six crew members and was on its way to the city of Holguin in eastern Cuba.
But it ploughed into a farm field soon after take-off and residents nearby reported sounds of an “explosion”.
Firefighters then tackled a fire coming from the destroyed aircraft, which had just left Jose Marti International Airport.
Photos showed the wings of the plane wedged between scorched trees and the main fuselage completely destroyed.
Government officials and Cuban president Miguel Diaz-Canel soon visited the crash site and told reporters there was “a high number of victims”.
He was quoted as saying: “There has been an unfortunate aviation accident. The news is not very promising, it seems that there is a high number of victims.”
He later confirmed the fire had been put out and authorities were identifying the bodies of the dead and that an investigation had been opened into the crash.
Gilberto Menendez, who runs a restaurant near the crash site, said he heard an “explosion” and “then saw a big cloud of smoke go up”.
An unnamed military officer called it a “disaster”.
Despite the reports of three survivors, a worker at Havana’s Calixto Garcia hospital told the Reuters news agency three people arrived at the hospital but one had died from burns and other trauma. They said the other two were in a serious condition.
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Six Mexican crew members were operating the flight, according to an employee of the small Mexican charter company Global Air, which is thought to own the aircraft.
The last major plane crash in Cuba took place in July 1997. An Antonov-24 passenger plane fell into the sea off Santiago de Cuba. All 44 on board were killed.