The temblor struck at a shallow depth, the US Geological Survey said.
"Based on all available data... the tsunami threat from this earthquake has passed and there is no further threat," the US Pacific Tsunami Warning Center said.
Earlier, the Tsunami Warning System had said waves as high as nearly 10 feet (three meters) were possible in some coastal areas of Cuba, while waves of up to three feet could hit Honduras and the Cayman Islands.
The Cayman Islands government had warned residents of coastal areas to move inland in a message on its website.
The initial tsunami threat warning included more than a dozen countries.
About three hours after the earthquake, US authorities warned that "minor sea level fluctuations" of up to 30 centimeters (11.8 inches) could still occur, but that any serious threat had passed.
A tsunami measuring gauge at Isla Mujeres, on Mexico's eastern coast, measured a wave with a maximum height of four centimeters (0.1 feet) after the earthquake, the US tsunami warning center said.
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