No injuries have been reported so far since the magnitude 7.7 quake hit.
Dr. Enrique Arango Arias, head of Cuba's National Seismological Service, told state media there had been no serious damage or injuries reported.
The Pacific Tsunami Warning Center initially warned the quake could generate waves up to three feet above normal in Cuba, Jamaica, the Cayman Islands, Honduras, Mexico and Belize.
Those who have witnessed the earthquake have shared videos and pictures on social media with one saying it was "the longest earthquake" he has ever experienced.
The quake was felt strongly in Santiago, the largest city in eastern Cuba, said Belkis Guerrero, who works in a Roman Catholic cultural center in the center of Santiago
She said: "We were all sitting and we felt the chairs move.
"We heard the noise of everything moving around."
She said there was no apparent damage in the heart of the colonial city.
"It felt very strong but it doesn't look like anything happened,'' she added.
Dr. Stenette Davis, a psychiatrist at a Cayman Islands hospital, said she saw manhole covers blown off by the force of the quake, and sewage exploding into the street, but no more serious damage.
Claude Diedrick, 71, who owns a fencing business in Montego Bay, said he was sitting in his vehicle reading when the earth began to sway.
"It felt to me like i was on a bridge and like there were two or three heavy trucks and the bridge was rocking but there were no trucks," he said.
He said he had seen no damage around his home in northern Jamaica.