"People should be aware that snowfalls are likely to cause widespread disruption to traffic especially about alpine passes and higher level roads, and more generally in Marlborough, Canterbury, Southland and around Dunedin," the bureau said.
"Exposed parts of the South Island east coast are likely to experience blizzard conditions for a time during Thursday and Friday, which will put stress on livestock and make outdoor pursuits hazardous."
MetService said it would issue warnings throughout the week for the "significant winter storm".
Bitterly cold Antarctic air would begin to sweep up the country from tomorrow, said MetService media and communications meteorologist Daniel Corbett.
"This has the potential to bring significant snow to the south and east of the South Island, as well as central and southern parts of the North Island."
Mr Corbett said the largest snowfalls were likely in inland Canterbury and Marlborough, and near sea level from Southland to Kaikoura by Thursday.
Mr Corbett said it was a "very dynamic weather situation" and details about where and how much snow was expected could change.
WeatherWatch head analyst Philip Duncan said the polar blast would bring heavy snow to the south and east coasts of both islands later this week, with snow to sea level in the South Island and near sea level in parts of the North Island.
"Nowhere in New Zealand can escape it. This is such a huge system."
The storm would hit the South Island tomorrow before spreading north over the entire country on Thursday and Friday. It would ease on Saturday before more rain and wind on Sunday.
Mr Duncan said Auckland could expect a "very cold" change with a high risk of hail, the chance of thunder, and possible snow flurries in the ranges.
He said the storm was almost identical to one in winter 2011 which saw snow falling but not settling in Auckland.
Snow was likely in the Coromandel and Kaimai ranges, but it was unclear whether it would get as far as the Waitakere, Hunua or Bombay ranges this time.
The polar blast prediction comes after heavy rain caused havoc in the South Island yesterday.
Roads flooded and schools were closed in Christchurch, and Dunedin was cut off from the north by flooding as Otago rivers ran at record highs.
MetService meteorologist Matthew Ford said there would be "patchy rain" for parts of the South Island today but "things have eased a bit today".
