There are 71 Dick Smith stores in New Zealand, according to the company's website, including 19 in Auckland. It is understood any staff affected by the restructure would be offered jobs elsewhere in the group.
Dick Smith has a total of 386 stores in Australia and New Zealand and the decision to shut a large number of them had been predicted by analysts because of poor sales.
As a result, the company will book a A$300 million provision in its accounts for the six months ended December.
Chief executive Grant O'Brien said he had already received a number of unsolicited approaches from would-be buyers.
"A divestment of Dick Smith will enable the Woolworths group to focus more investment on serving customers in its core business," Mr O'Brien said in a statement.
Mr Smith said he feared the chain would be sold to a foreign-owned company.
"I'll rubbish them the whole time. They wouldn't want to pay much," he told the Sydney Morning Herald.
He later told AAP he would not go that far and warned the Woolworths' decision was a sign Australia was moving closer to the point when everything would be foreign-owned.
Mr Smith said although it made commercial sense for Woolworths to get rid of the electronics stores which were no longer making money, he believed selling it to a foreign investor would mean "further destruction of Australia".
"This is just continuing where all the wealth is going overseas and damaging our country," he said.
The Buy Australian campaigner believed the local market was not big enough to provide sustained profits for companies in an increasingly globalised world.
"When you want endless growth only the biggest survive," Mr Smith said. "Little Australia won't have any ownership at all."
The entrepreneur founded the Dick Smith business in Sydney in 1968. He ensured the profile of the company grew through quirky advertisements and publicity stunts.
By 1980, the chain had grown to 20 stores and Mr Smith sold 60 per cent of his company to Woolworths. The supermarket retailer bought the remainder of the company two years later.
News of Woolworths' decision to sell the business came as the retailer reported its first-half sales had risen 5 per cent to $29.7 billion despite subdued consumer confidence and falling prices.