The epicenter of the earthquake was about 72 miles northwest of Lucea, Jamaica, at a depth of 6.2 miles.
"It is unlikely the Cayman Islands will be impacted by a damaging tsunami. There is now very low risk. Information from the Tsunami Warning Center indicates the first wave would have already passed the Cayman Islands. The main threat now relates to the possibility of aftershocks," tweeted Hazard Management Cayman Islands.
"So far there have been 13 aftershocks recorded in the Cayman region," it added.
Until now, no deaths or injuries have yet been reported.
ILKHA