The quake struck at a depth of 17 kilometres about 57 kilometres southwest of El Cobre and about 66 kilometres west-southwest of Santiago de Cuba.
It was the first earthquake of that strength in the vicinity of Cuba since the first quarter of 2014, when three quakes shook Cuba and the Florida Keys in the first three months of 2014.
The strongest was a 5.1-magnitude tremor in early January; all of those three quakes were also felt in Florida. While much of the Caribbean is a seismically active region, earthquakes have largely been rare in Cuba.
There were not yet reports of any damage or injuries resulting from the quake, which occurred at around 7 p.m. local time.