The city of Christchurch and several other districts on New Zealand's South Island have declared a state of emergency after being hit by the remnants of Cyclone Gita.
Dozens of schools have been shut and roads closed in the South Island as the storm made landfall on Tuesday.
Air New Zealand has cancelled all flights in and out of the capital, Wellington, in the North Island.
Residents were told to expect floods and winds of up to 150km/h (90mph).
The Grey District, Buller District and Nelson Tasman are among the regions in the South Island to have declared a state of emergency, as has Taranaki in the North Island.
"The full impact of the storm will be felt overnight and tomorrow morning," said Christchurch Mayor Lianne Dalziel.
She urged residents in low-lying areas to evacuate, saying: "We are expecting homes to be flooded."
The Buller District Mayor Garry Howard said he expected high seas and strong winds in the West Coast region. "This is not a good situation for those in seafront properties," he said.
Gita, which was downgraded on Tuesday from a tropical cyclone to a storm, is already causing flooding in parts of the South Island with waves up to 7m (22ft) high.
Community halls in Christchurch and other districts are providing shelter for those affected by the weather.
Several tourists reportedly had to be rescued by authorities after becoming stranded on roads near Whataroa, the New Zealand Herald reports.
Footage published on local news websites showed powerful winds slamming the West Coast on Tuesday afternoon, damaging properties.
Meanwhile, trucks delivered sand to the areas at risk of flooding with residents queuing to fill bags to stack around their homes in the hope of protecting their belongings.
Prime Minister Jacinda Ardern said earlier that troops had also been sent out to areas that were likely to be hardest hit by the storm. She added that the national Civil Defence office in Wellington were also on standby.
"My message still to people is please look out for your local warnings and expect disruption to travel and please just be careful," she told reporters at parliament.
Gita last week left a trail of destruction in the Pacific island nations of Tonga and Fiji.
Tonga in particular is reeling from the storm, which injured people and destroyed buildings including the parliament.