Hayman has been suffering with an infected toe and despite a course of antibiotics it has failed to heal.
Greg Somerville will take over as tighthead prop for the match at Wellington's Westpac Stadium, while Campbell Johnstone, who had been on standby, has been called on to the bench.
"Carl's been on a course of antibiotics this week to deal with an infection in his foot," said All Blacks coach Graham Henry.
"He is responding to treatment, but it is a slow process. We were hopeful he would come right in time to play this weekend, but that is not the case.
"We are fortunate to have a player of Greg's quality who can step in."
New Zealand team: Mils Muliaina; Rico Gear, Tana Umaga (capt), Aaron Mauger, Sitiveni Sivivatu; Dan Carter, Byron Kelleher; Tony Woodcock, Keven Mealamu, Greg Somerville, Chris Jack, Ali Williams, Jerry Collins, Richie McCaw, Rodney So'oialo.
Reserves: Derren Witcombe, Campbell Johnstone, Jono Gibbes, Sione Lauaki, Justin Marshall, Ma'a Nonu, Leon MacDonald.