The quake, which hit at 5.09pm on Sunday, was centred 20km east of Seddon in the Cook Strait at a depth of 17kmcell phone cases.
It follows a magnitude 5.7 on Friday, a 5.8 on Sunday morning and numerous aftershocks - many magnitude 4 and greater otter case.
Parts of parliament, other Wellington buildings and CentrePort have been damaged. A chunk of concrete fell from a building on Featherston St and shipping containers reportedly toppled.
Buildings were evacuated, including TSB arena on Wellington's waterfront and the Mercure Hotel.
The quake toppled shelves and items in homes. It shook stock off shelves in shops.
One person suffered minor injuries in the quake, Wellington Civil Defence says.
There has been structural damage to buildings, broken glass and burst water mains around Wellington, police central communications Inspector Marty Parker told NZ Newswire.
Power and phonelines were down in a few areas.
Mr Parker urged people to check on their neighbours, especially elderly, and make sure to have battery powered torches and radios overnight.
"If you are driving around, just be aware there may be damage on the roads or debris that we aren't aware of."
Police have closed hazardous parts of roads in the CBD and Civil Defence advised people to stay home.
Phonelines are overloading and people are urged to send text messages instead of calling fr4 pcb.
The Fire Service had about 60 callouts around Wellington and the Hutt Valley, including ceiling panels that fell down after a pipe burst in a Hutt Hospital building and three groups of people rescued from lifts, a spokeswoman said.
The worst damage appeared to be to the walkway between James Smith carparking building and the Michael Fowler Centre, which has pulled away and damaged water pipes in the Wellington City Council, she told NZ Newswire.
There had been one report of a powerline down in Tasman, she said.
Blenheim police said there were slips on State Highway 1 and reports of damage around Marlborough.
Blenheim resident Pete Jones described the quake as a slow rolling shake rather than a sharp shock.
Tranz Metro has cancelled all trains around Wellington until further notice label sticker, while Wellington Airport was closed temporarily for checks to take place.
Some businesses have told staff to be prepared to work from home on Monday.
GeoNet says earthquake swarms had happened in the same part of the country previously and continued for days.
"We just can't predict when they will die away completely."
There is no risk of a tsunami.
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