The earthquake's epicentre was about 40km north of Te Anau, which is the gateway to the tourist hotspot of Fiordland, according to New Zealand's National Emergency Management Agency (NEMA).
There were no immediate reports of injuries or damage.
The quake struck after 9pm on Thursday.
Authorities initially assessed its strength at magnitude 6.3, with NEMA issuing a tsunami warning and urging people in coastal areas to evacuate.
It later downgraded the warning to an advisory after the magnitude was revised to 5.9 before cancelling it altogether, saying the threat had passed after no tsunami signals were detected for two hours following the quake.
Local resident Maylene Puyat, the duty manager at Te Anau's Fiordland Hotel, told Reuters the earthquake was "a bit strong" and shook the building for about a minute.
"In the hotel, it's shaking," she said.
Another resident told local outlet Otago Daily Times the earthquake shaking was "long and loud" and sounded "like a train".
"The walls were definitely moving," they said.
More than 20,000 "felt reports" were sent to hazard monitoring system GeoNet.
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