The tremor was recorded north-west of a largely uninhabited and remote Norwegian island, officials said.
No injuries or damage were immediately reported.
The Norwegian earthquake centre Norsar said the quake was recorded in the sea between the volcanic island of Jan Mayen and Greenland.
The tremor was centred some 74 miles off Jan Mayen at a depth of approximately 6.2 miles.
Norwegian news agency NTB said there were 18 people on the island - military and meteorological institute staff - who were woken by the quake.
Silje Wennesland told NTB that "I had my heart in my throat when I woke up because the mirror and the cabinets shook".
Norsar said aftershocks are expected but no tsunami warning was issued.
"Fortunately, no one was injured, and everyone is fine, but we noticed it," Ms Wennesland told NTB.
"It has happened before, and this was quite powerful," she said, adding the tremor lasted for 30 seconds.
Norsar said the quake was one of the strongest registered.
Since 1970, about 10 quakes have been registered in the region with a magnitude of 6 or higher.
The previous such quake was recorded on August 30 2012, and had a magnitude of 6.6.
