Fairfax Media confirmed on Monday it will sell its remaining stake of 51% in Trade Me.
The company has entered an agreement with UBS to sell its majority stake.
The New Zealand stock exchange on Monday suspended trading in Trade Me shares at the request of the company.
Trading was suspended to facilitate what is known as a book building process. This is an organised accumulation of the total number of offers that are available from investors.
A halt has also been requested on the Australian exchange.
The shares will be offered for $A3.05 each, raising $A616 million.
The Sydney Morning Herald said on Monday that investment bank UBS has been appointed to sell the shares.
AAP reports trading in Trade Me closed in Australia at $A3.22 on Friday.
Trade Me is a New Zealand online business, which Fairfax acquired for $NZ750 million in 2006.
"The proceeds from the sale will reduce Fairfax's net debt and will provide us with a very strong balance sheet and the financial flexibility to invest and to complete the company's structural transformation," Fairfax chief executive Greg Hywood said in a statement on Monday.
AAP reports Fairfax had net debt of $A914 million at June 30, 2012.
"Trade Me has been a great business for Fairfax and we have learned a great deal more about the successful operation of digital businesses over the years we acquired Trade Me," Mr Hywood said.
Independent media commentator Peter Cox said while Trade Me had a big market share in New Zealand its rate of growth was slowing in a maturing market.
"Even though I would agree that you are looking for businesses for the future that are internet based where there can be high rates of growth, I would suggest that this one has probably seen its best days now," Mr Cox said on Sunday.
"Therefore if they can get what they feel to be a very good price for it then definitely they should consider selling it."
Fairfax bought Trade Me for $NZ700 million in 2006 and floated 34% of the company in December 2011 through an initial public offering which raised $NZ363 million.
A further 15% was sold in June 2012 for $NZ206 million.
AAP reports a sale would give Fairfax the opportunity to bolster its balance sheet - the company's net debt was $A914 million at 30 June, 2012.
Mr Cox said $A650 million would "put a nice dent in the debt at Fairfax".
"It also puts them in the position where if there came an opportunity for what they considered to be a good investment, they would have the funding ability from which to invest in something," Mr Cox said.
Tower Investments chief executive Sam Stubbs says the sale is good for New Zealand shareholders.
"Its weighting in the index will now double from about 2% to 4% and that takes it into the top six companies in New Zealand. And what that typically means is you'll get institutional buyers coming in and buying the stock to get to at least index weight."
Business consultant Lance Wiggs said Fairfax has more than doubled the money it invested in Trade Me.
Mr Wiggs said it is suprising Fairfax had decided to sell its entire stake in the online auction site, because it leaves the company without a strong revenue generating arm.
Earlier in 2012, Fairfax announced 1900 job cuts, closure of printing presses in Sydney and Melbourne and creating online paywalls in response to weak advertising markets and structural changes to the media industry
Trade Me was founded in New Zealand by Sam Morgan.