The Norwegian earthquake centre NORSAR said it was recorded at 2.49am on Friday in the sea between the volcanic island of Jan Mayen and Greenland, a Danish territory.
No injuries or damage were immediately reported.
Norway’s 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: “I had the heart in my throat when I woke up because the mirror and the cabinets shook.”
"Fortunately, no one was injured, and everyone is fine, but we noticed it," Ms Wennesland added.
"It has happened before, and this was quite powerful," she said, adding the tremor lasted for 30 seconds.
NORSAR said aftershocks are expected but no tsunami warning was issued.
According to the centre, it was the strongest earthquake recorded in Norway, with the previous record being a 6.6-magnitude quake recorded in Van Mayen on 30 August, 2012. That earthquake caused no injuries, but did do some material damage.
Jan Mayen is regularly exposed to earthquakes, the centre said, and has registered around 10 shocks with a strength above magnitude 6 since 1970.