Based in Australia, Fairfax owns The Dominion Post and The Press newspapers, and the websites stuff.co.nz and TradeMe in New Zealand, as well as a number of regional newspapers.
Mr Kirk will leave the company immediately. Brian McCarthy has been named as acting CEO, according to a company statement to the Australian stock exchange.
Mr Kirk, who had been at the Fairfax helm since 2005, also issued a statement to end a period of speculation over his future.
"It has been a privilege to lead Fairfax Media during this period of great change and challenge for media companies all over the world," Mr Kirk said.
"A lot has been achieved and I thank especially the board and the many managers throughout the business who have contributed to the re-positioning of Fairfax Media for continued success in the future."
A Rhodes Scholar, Mr Kirk captained the All Blacks to their only World Cup victory, in 1987.
Shares of Fairfax Media immediately soared, gaining 9 cents to $A1.58.
Fairfax chairman Ronald Walker announced the resignation but provided no explanation.
"During his more than three years in the role, David has been an outstanding CEO of Fairfax Media," Mr Walker said in a statement.
"He and his team have led the complete re-positioning of the company, from a metropolitan newspaper publishing business to a position in which the company is now clearly the leading media company in Australasia."
Mr Walker said Mr Kirk had helped operational improvements including cost reductions and achievement of all synergies from acquisitions as well as growth of circulations at the major metropolitan newspapers.
