It was recorded at a shallow depth of 10km (6 miles), just 211km (140 miles) west of the sub-Antarctic Auckland Island, off New Zealand’s South Island.
No tsunami warnings have been issued yet.
Residents of Balclutha, Gore, Invercargill, Lumsden, Roxburgh, Te Anau and Tuatapere will have felt minor tremors.
A second quake was reported shortly afterward, with New Zealand’s capital city Wellington jolted by 5.0 magnitude tremors.
It is reported to have hit at a depth of 31km and 30km, northeast of Seddon.
People remove debris of a building which comes just hours after Mexico City was hit by a quake measuring 7.1 on the Richter Scale.
Fires broke out across the city as footage showed black plumes erupting over the city’s skyline following the quake at 1pm local time yesterday.
This came just a week after another quake hit the country that killed more than 90 people.