The United States Geological Survey (USGS) indicates that a strong shake was felt at the epicentre of the quake.
The quake was reportedly at a depth of 29.3km (18.21 miles).
The Joint Australian Tsunami Warning Centre has now said that Australia is on tsunami alert.
But the US Tsunami Warning System has indicated a tsunami will likely pose little threat following the quake.
This includes to Macquarie, surrounding island territories as well as mainland Australia.
The USGS originally registered the quake as having a magnitude of 7.3, but later revised this figure to 6.7.
Macquarie Island lies about halfway between New Zealand and Antarctica, and has been a part of Tasmania, Australia, since 1900.
This is a breaking story. More to follow.