Though the Office of Disaster Preparedness and Management did not immediately report any loss of life, a Special Anti-Crime Unit conducted aerial reconnaissance of the northern and eastern parts of Trinidad.
The ODPM reported an electricity disruption island-wide in Tobago but only portions of the island of Trinidad.
Water service also was cut off to large areas in the north and east of Trinidad.
The quake was followed some five hours later by a moderate aftershock of 5.5 magnitude.
Early media reports said the entire island of Tobago and the southern and northern ends of densely populated Trinidad were without electrical power.
Frightened citizens told radio stations of superficial damage to homes, offices and government buildings.
The earthquake disrupted traffic at the country's national airport as travelers and workers were evacuated from Piarco National Airport.
Workers of the Trinidad and Tobago Electricity Company were dispatched to repair damage to lines in and around the capital.
Venezuela's seismological institute said the quake weighed in at 6.1 and hit just north of the island of Trinidad, which lies just off Venezuela's northeastern coast.
The tremors were felt throughout most of eastern Venezuela, but there were no immediate reports of major damage there, Gustavo Malava, director of Venezuela's seismological institute, told Venezuela's state-owned VTV television.
The US Geological Survey's National Earthquake Information Center said in a statement that the temblor struck at 1308 GMT, 41 kilometers (26 miles) northwest of Port-of-Spain, at a depth of 63 kilometers (39 miles).
The aftershock followed at 18:23 GMT with an epicenter at nearly the same spot at a depth of 90 kilometers (56 miles).
Trinidad and Tobago is among the Caribbean's more prosperous nations. Its economy depends largely on oil and petrochemicals. Tobago is more dependent on tourism.
The quake rocked Port-of-Spain and the north of Trinidad, shaking buildings for 15 seconds, according to The Trinidad and Tobago Express. Other local media cited reports of cracking structures, building evacuations and power outages.
The USGS magnitude-6.0 quake reading was based on the open-ended moment magnitude scale, often used by US seismologists, which measures the area of the fault that ruptured and the total energy released.
