Rafael is the 17th named storm of the season.
Several nearby structures also were damaged, including the historic Marti Theater and the Calvary Baptist Church.
The Trump administration is banning charter flights to Cuban cities besides Havana in a new tightening of U.S. restrictions on the island.
A government meteorologist says the tornado that struck Havana was a Category F3, with winds between 155 and 199 miles per hour.
A Cubana Airlines Boeing 737 has crashed on takeoff from Havana's José Martí International Airport, according to state-run television. An airport sources says casualties are reported.
The Obama administration has granted permission for the first U.S. airlines to start the first scheduled flights to Cuba in more than five decades.
The first U.S. cruise ship in nearly 40 years has crossed the Florida Straits from Miami and docked in Havana, restarting commercial travel on waters that served as a stage for a half-century of Cold War hostility.
In his historic visit to Cuba, President Barack Obama is relegating decades of American acrimony with the communist country further into the past and cementing a new relationship between the Cold War-era foes.
President Barack Obama says the reopening of embassies in Havana and Washington is another demonstration that the U.S. doesn't have to be imprisoned by the past.
The Obama administration on Friday formally removed Cuba from a U.S. terrorism blacklist as part of the process of normalizing relations between the Cold War foes.