A magnitude 4.5 earthquake in Fiordland gave some South Island residents an early morning wake-up on Sunday.

The offshore quake, centred 20km north-west of Milford Sound at a depth of 12km, struck at 5.58am.

Geonet said it was felt in Fiordland, Queenstown and Dunedin.

The earthquake followed a 5.7 jolt near Turangi in the centre of the North Island on Saturday.

The quake was not widely felt by locals when it struck 10 kilometres south of the town at a depth of 90km at 12.50pm.

However, it was felt as far south as Wellington.

On Tuesday night, a magnitude 7 quake which struck off the Taranaki coast was felt around the country but did no major damage.