Several neighbourhoods in the city have been badly affected by the cyclone, which was swept in from the Gulf of Mexico on Sunday evening, according to local media reports.
Cuban president, Miguel Diaz-Canel, announced on Monday three people had been killed, while dozens more were being treated for injuries.
“The damage is severe, so far we regret the loss of 3 human lives and treated 172 injured,” he wrote on Twitter.
Photographs circulated online showed roofs torn off buildings, upturned cars and flooded streets in several Havana neighbourhoods.
Reports stated several districts in the city were experincing power cuts, while some areas also saw isolated landslides. Winds are thought to have reached in excess of 60mph.
He said residents from across the city had called to report the cyclone had made landfall late on Sunday evening.
“People heard what sounded like a jet engine and felt changes in environmental pressure,” he added.
Tornados are a relatively rare occurrence in Havana, although the city has been hit by the weather phenomenon in the past.
The most famous disaster came in December 1940 when a tornado swept through the city, killing 20 people and injuring more than 200 others in the nearby town of Bejucal.
Join our commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies