An initial 6.5-magnitude quake struck at 1804 GMT off the island of Espiritu Santo in the north of the archipelago at a depth of 10 kilometres, the US Geological Survey said.
An aftershock with a magnitude of 5.4 rocked the island shortly after.
The Pacific Tsunami Warning Centre said there was “no tsunami threat” from the initial quake.
With Cyclone Kevin also raging, government spokesman Joe Harry Karu told AFP a state of emergency had been declared by the council of ministers.
Pacific Red Cross spokesman Soneel Ram told AFP no casualties had so far been reported.
When the earthquakes struck Friday, locals were hunkering down as fierce winds from the cyclone tore roofs from buildings and uprooted trees.
Only two days earlier, Cyclone Judy had lashed Vanuatu with winds up to 200 kilometres (125 miles) per hour.
Torrential rain had flooded roads while electricity and communications are still affected across the island nation, home to 320,000.
Dickinson Tevi, secretary general of the Vanuatu Red Cross Society, warned of the possibility of significant damage.
“People on (Espiritu) Santo felt the earthquake, but couldn’t go outside to assess the damage because of the high winds,” Tevi told AFP from the capital Port Vila.
“They told me they didn’t sleep well as the earthquake hit when they were already awake from the cyclone.”
He said parts of Port Vila have been without power for two days.
“Once the winds have died, we will assess the situation, but there is likely to be significant damage as Cyclone Judy had already damaged many structures.”
In January, a 7.0-magnitude earthquake also struck off Espiritu Santo, sending villagers fleeing to higher ground but causing no major damage.
Vanuatu is in the Pacific “Ring of Fire”, where tectonic plates collide, and experiences frequent seismic and volcanic activity.
It is ranked as one of the countries most susceptible to natural disasters like earthquakes, storm damage, flooding and tsunamis, according to the annual World Risk Report.