The US Geological Survey said the quake hit at a depth of 29 kilometres and was centred about 100 kilometres north-east of the main island in the early morning hours of Monday local time.
Hours later, a second 6.1 magnitude quake hit in the same area.
The Pacific Tsunami Warning Center in Hawaii issued an alert following the first quake saying hazardous waves could be possible but later said there was no longer a tsunami threat.
A warning was also cancelled hours later by the country's disaster management office.
Tsunami sirens could be heard after the 1:18am quake urging residents to move inland, in a live video streamed by the Tongan Broadcasting Commission.
People in the capital, Nuku'alofa, were seen moving inland or to higher ground before officials gave the all-clear for residents to return home.
There were no initial reports of casualties, TBC said.
Tongans posting on social media reported being able to place calls with most of the inhabited island chains that make up the country.
It was too soon to know the extent of any damage, which would be assessed in daylight, the broadcaster added, but none was immediately reported.
Tongan taekwondo athlete Pita Taufatofua posted to Facebook that items fell from shelves and tables and pictures fell from the walls during the shaking.
"Was hard to stand up," he wrote.
"Never felt an earthquake go for that long."
Tonga is a country in Polynesia made up of 171 islands with a population of just over 100,000 people, most of whom live on the main island of Tongatapu.
It is 1800 kilometres north east of New Zealand and situated on the Pacific Ring of Fire, a tectonic region of earthquakes and volcanoes.
The low-lying island nation was devastated by a tsunami in 2022 that was prompted by a volcanic eruption.
Three people were killed in that disaster.
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