The quake was felt across northern Central America, prompting a tsunami warning in Puerto Rico, and the Caribbean Islands, but little damage and no casualties have been reported.
Tsunami advisories have been issued for some Caribbean nations, but not the Bahamas, after an natural disaster in the region on Tuesday night.
The powerful quake was initially measured at 7.8, but later revised. People near the coast of those nations should seek higher ground immediately. The temblor set of tsunami warnings that were canceled and hour later.
The tremor struck in the sea about 125 miles (202km) north-northeast of Barra Patuca, Honduras, and 188 miles (303km) south-west of George Town, Cayman Islands.
A tsunami advisory signals a threat to those in or near water, as strong currents and waves could be risky.
The northern coast of Honduras closest to the quake's epicentre is sparsely populated, with much of it covered by nature reserves.
Honduran President Juan Orlando Hernandez urged citizens to "stay calm, report emergencies and follow the instructions of authorities". The tremor occurred about 6 miles (10km) below the surface.
The Swan Island quake was one of the strongest to strike the Caribbean since recordkeeping began.
The shallow natural disaster was recorded at 9:51 p.m. with its epicenter 450 kilometers east of Mahahual, Quintana Roo, at 17.5 n, 83.6 w, at a depth of 33 kilometers and a magnitude of 7.5.