There was no tsunami threat from the quake, Civil Defence said.
Although the true quake was offshore, it was felt by people around the South Island.
Laura Todd, who works at Invercargill's Top 10 Holiday Park, said the quake was "a big one" and had left her "a wee bit shaky".
"I was just in the office loading up all our bookings when I thought, gosh everything's just starting to move. I looked up and the lights had started swaying. It was a really long rolling earthquake."
The quake lasted around a minute, she said, but it was rolling rather than rough and nothing had been damaged.
Campers at the park ran outside when the quake struck.
"A lot of them have never felt earthquakes before so they got a bit of a fright," she said.
Residents from the South Island have shared their experiences on social media. Many reported swaying or shaking that lasted for more than 30 seconds and set light bulbs swinging.
Fire and Emergency New Zealand had received no reports of structural damage, a spokesman said, but the quake was felt at the fire station in Invercargill.
One person reported their car had sunk into liquefaction at their property in the Invercargill suburb of Glengarry but it appeared to have been "more or less a false alarm", he said.
"The fire crew have described it as one car stuck in the mud. So as far as we can tell it had very little if anything to do with the earthquake."
Neither the Snares Island and the Auckland Islands have permanent inhabitants, although scientists sometimes visit for research purposes.
The Snares Islands are the northernmost of the country's subantarctic islands and one of the "most untouched and pristine areas in New Zealand", according to the Department of Conservation, because introduced land mammals were never established there.
They lie around 100km south-west of Stewart Island.
The Auckland Islands lie 465km south of Bluff, and are the country's largest subantarctic islands. They are made up of the remains of two ancient volcanoes.
The islands are now predominantly conversation land with a marine mammal sanctuary established in 1993 and a marine reserve classification in 2003.