It forced him to quit the game and he had a kidney transplant in 2004, but the organ stopped functioning in 2011.
"Jonah was a legend of our game and loved by his many fans both here and around the world," said New Zealand Rugby chief executive Steve Tew.
"We're lost for words and our heartfelt sympathies go out to Jonah's family."
Family spokesman John Mayhew told New Zealand television that Lomu's death was "totally unexpected" and that he had only arrived back from the UK on Tuesday, after spending time there for the Rugby World Cup.
New Zealand Prime Minister John Key said: "The thoughts of the entire country are with his family."
In an interview with the Daily Mail in August, Lomu had said he was on dialysis and hoping for a second kidney transplant.