The earthquake struck at 6:23pm local time on Saturday and was measured at a magnitude of 7.6 and occurred at a depth of 10km, according to the United States Geological Survey (USGS).
The quake's epicentre was located about 200km south-southwest of George Town in the Cayman Islands, USGS said.
It was unclear if there was any damage on land.
This marks the biggest quake in the region since 2021, when a 7.2 magnitude earthquake struck Haiti, according to the US National Oceanic and Atmospheric Administration
The US Tsunami Warning System said a tsunami warning was in effect following the quake for the Caribbean Sea and north of Honduras, adding that a tsunami was not expected on the US Atlantic or Gulf Coast.
The US National Tsunami Warning Center said there is no tsunami alert for the US mainland but issued a tsunami advisory for Puerto Rico and the US Virgin Islands.
Hazard Management Cayman Islands urged residents located near the coast to move inland and to higher ground. It said wave heights of 0.3 to one metres were expected.
Puerto Rico Governor Jenniffer González Colón said in a statement she is in contact with emergency agencies after the tsunami advisory, but did not recommend anyone to leave the coast.
The Dominican government also issued a tsunami alert and recommended residents on the coast to move to high areas "of more than 20 metres of altitude and two kilometres inland".
It also urged ships to steer away or avoid entering the sea for the next few hours.
The Cuban government requested people to leave beachfront areas.
Honduran authorities said are no immediate reports of damages, but urged its residents to stay away from beaches in the next few hours.
Later, the US government's National Oceanic and Atmospheric Administration (NOAA) said "tsunami waves reaching 1 to 3 meters above the tide level are possible along some coasts of Cuba".
It added waves between 0.3 and one metre above the tide level are possible for some coasts of Honduras and Cayman Islands.
"Actual amplitudes at the coast may vary from forecast amplitudes due to uncertainties in the forecast and local features," the NOAA said in a report.
with dpa
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