The USGS said the quake was at a depth of 15.2 kilometres and an aftershock measuring magnitude-5.7 had also been recorded.
The Pacific Tsunami Warning Centre has withdrawn a tsunami warning for parts of the Pacific located 300 kilometres from the epicentre.
Radio New Zealand reported people had been evacuating the Fijian tourist hub of Nadi since the earthquake struck.
There have been no reports of damage or injury from Fiji.
"We felt it [the quake] ever so slightly in Suva," Sune Gudnitz, head of the United Nations' Office for the Coordination of Humanitarian Affairs said.
Red Cross Australia aid worker Susan Slattery said "pretty much everybody in Suva" evacuated buildings for higher land after the quake, fearing a tsunami.
"Certainly the whole city was on the move," she said.
"There are some level of earthquakes in and around Fiji fairly constantly or fairly often but this level of earthquake is unusual and certainly this close to the main islands is unusual and having the resultant tsunami warning is not common."
Kelvin Anthony said he was working in an office building in central Suva when a "slight tremor" was felt.
"Before the advisory came, one of our managers, who has sort of had, I guess, previously been in situations like this, quickly advised everyone that that's an earthquake and that we've got to move," he told the ABC.
"We also had power cuts, so it went on off, on off, about two or three times."
Spiro Spiliopoulos, senior seismologist at Geoscience Australia, said the tremors happened close to a tectonic plate boundary between the Australian plate and the Pacific plate, where a large number of earthquakes are recorded.
"This is unusual in that it occurred a little bit away from the plate boundary," he told the ABC.
"They have the potential to generate tsunamis."
Geoscience Australia said main tremor would have been felt in the Pacific islands of Vanuatu, New Caledonia, Tonga and parts of American Samoa.
A magnitude-6.3 quake hit 582 kilometres south of Suva on Monday at a depth of 555 kilometres.