Three people have survived but are in a critical condition, Cuban Communist Party newspaper Granma reported.
The plane was carrying 110 passengers and crew, according to the Mexican firm from which the plane was leased.
Two days of national mourning have been declared, after Cuba’s worst air disaster since the 1980s.
There were six Mexican crew members on board; the passengers were mainly Cuban, with five foreigners among them, state-run website Cubadebate reports.
“There has been an unfortunate aviation accident. The news is not very promising, it seems that there is a high number of victims,” Cuban President Miguel Diaz-Canel said after visiting the crash site.
The plane had been leased to state airline Cubana de Aviación by the Mexican company Aerolineas Damojh.
The Mexican authorities said the plane was built in 1979 and had been successfully inspected last November.
Aerolineas Damojh, also known as Global Air, has three planes in operation.
Boeing said that it was ready to send a technical team to Cuba, “as permitted under US law and at the direction of the US National Transportation Safety Board and Cuban authorities”. A US trade embargo has been in force against Cuba for many decades.