The 40 passengers included 22 foreigners from Spain, Argentina, the United States, France, the Netherlands, Britain, Canada and Mexico, according to the daily Venceremos and the ACN news agency. Six of the injured victims were in critical condition.
Details about the names and nationalities of those injured or killed in the deadly crash have yet to be released.
The UK Foreign Office said it was "seeking information from the Cuban authorities" and that it was "ready to assist any British people who require our help", a spokesperson told the BBC.
Radio Guantánamo said it had spoken to the driver of the bus who said he lost control of the bus in wet conditions on a bendy section of the road between Baracoa and Guantánamo.
Cuban highways are poorly lit, narrow and rutted with huge potholes.
The bus was carrying tourists and local travellers in the far east of Cuba, on a road between the cities of Baracoa and Guantanamo.
"We are now providing assistance to two British nationals who were injured on the bus".
Thursday's wreck is the fourth major bus accident in a month.