The Boeing 737-200 was leased by Cubana de Aviacion from the Mexico-based Aerolineas Damojh for a domestic flight to the eastern Cuban city of Holguin.
The 39-year-old jet came down in the early afternoon in a field just outside the international airport. Witnesses told the state Granma newspaper it had veered to one side before striking a power line.
Four passengers, a man and three women, were said to survive the accident. The man died of his injuries soon after he was rescued from under the debris.
The three women were taken to a Havana hospital with burns and fractures and are in a critical condition. They are reportedly in intensive care. Cuba TV initially said one of them died, but then withdrew the report.
The Cuban government has declared a period of mourning starting Saturday until Sunday midnight as search continues for the jet’s two flight recorders.
Cuban leader Miguel Diaz-Canel, who went to the crash site, told Cuban television a transport ministry commission was looking into the cause of the crash. Boeing, the US aircraft maker, offered Cuba assistance of its technical team.
A flight engineer on another Cubana airliner that took off from Havana airport 13 minutes before the crashed plane told Cubadebate a technical fault had mostly likely caused the accident.
Cuba’s former leader Raul Castro said he was following the incident and sent condolences to the victims’ families, according to the publication. Local media said he was still recovering from a recent hernia surgery.
The Friday air disaster was the Cuban carrier’s first in almost 20 years since its Yak-22 plane hit the ground in December 1999 miles from the Spanish city of Valencia, killing 22 passengers and crew. Earlier, on 3 September 1989 Cubana de Aviación's Il-62M crashed shortly after takeoff from José Martí International Airport due to bad weather. All 126 people onboard the aircraft and 24 people on the ground died in the disaster.