State TV said the jet veered sharply to the right after takeoff.
Cuban President Miguel Diaz-Canel said "There is a high number of people who appear to have died," from the scene.
He further added, "Things have been organized, the fire has been put out, and the remains are being identified." Relatives of those aboard were ushered into a private area at the terminal to await word on their loved ones.
The Boeing 737 went down just after noon a short distance from the end of the runway at Jose Marti International Airport while on a short-hop flight to the eastern city of Holguin. Firefighters rushed to extinguish the flames that engulfed the jet. Cuban media reported three survivors.
Authorities said there were 104 passengers and nine crew members on the flight, operated by Cubana, the Cuban state airline.
On Thursday, Cuban First Vice President Salvador Valdes Mesa met with Cubana officials to discuss improvements to its service. The airline blames its spotty record on a lack of parts and airplanes because of the US trade embargo against the communist island.
(with input from agencies)