Flight tracking websites indicate the plane departed at mid-morning local time, and it reportedly crashed shortly after.
The plane was carrying 104 passengers, according to local media.
"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.
State TV said it was an internal flight from the Cuban capital to the city of Holguin, in the east of the island.
The airliner had been leased to state airline Cubana de Aviación by the Mexican company Aerolineas Damojh, a statement from the Mexican government said.
It said the plane was built in 1979 and had five Mexican crew members on board, including the pilot and co-pilot.
The plane had been successfully inspected last November, according to the Mexican transport ministry.
Images showed a thick column of smoke rising above the crash site as fire crews and ambulances attended the scene.
Radio Havana Cuba said on Twitter that the plane came down on the "highway" between Boyeros and Havana, near the airport.
According to industry research, last year was the safest in history for commercial airline travel with no passenger jet crashes.
But there have been several serious air disasters this year. Last month, a military plane crashed shortly after take-off in Algeria, killing more than 250 people.
