The powerful tremor struck 72 miles (117 km) northwest of the coastal town of Lucea at a relatively shallow depth of around six miles (10 km), the US Geological Survey (USGS) said.
The International Tsunami Information Center warned that "hazardous tsunami waves" could occur "within 186 miles (300 km) of the epicenter along the coasts of Jamaica... Cayman Islands and Cuba."
Waves of up to three feet (1m) could also land on the coasts of Mexico, Belize and Honduras, it added.
The quake was centred in the sea, 86 miles (139 km) northwest of Montego Bay and around the same distance from Niquero, Cuba.
It was initially measured at 7.3 magnitude before being upgraded.
Buildings shook in Miami, the Miami Herald newspaper reported, while several South Florida buildings were being evacuated as a precaution, city officials said.
in Cuba, officials said there were no immediate reports of damage or injuries.
The quake could be felt strongly in Santiago, according to Belkis Guerrero, who works in the centre of the city.
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