The fly-half star is suffering from a hamstring problem and will be replaced by Aaron Cruden as New Zealand go for a Test series whitewash following victories in Auckland and Christchurch.
Elsewhere, number eight Kieran Read is sidelined through concussion, so skipper Richie McCaw switches from openside flanker and will forge a back-row combination alongside Liam Messam and Sam Cane.
There is also a Test debut for lock Luke Romano, while wings Hosea Gear and Ben Smith gain opportunities instead of Zac Guildford and Julian Savea.
"Dan pulled up with a sore hamstring after training on Tuesday," All Blacks coach Steve Hansen said.
"On assessment, he has suffered a mild hamstring strain to his right leg which has unfortunately ruled him out of this weekend's Test.
"He will undergo further assessment over the next few days to determine when he will be fit to return to rugby."
Carter's late drop-goal edged New Zealand to victory last weekend, and Hansen added: "It was a tough, high-pressure Test.
"It said a lot about the character of both teams, and I believe this third Test will see the same character and composure needed.
"The All Blacks, by their own admission, weren't happy with the way they performed on Saturday, and in part this is a credit to the way the Irish played.
"They have laid down a challenge, and the key will be now how we respond."
New Zealand team: I Dagg; B Smith, C Smith, S B Williams, H Gear; A Cruden, A Smith; T Woodcock, A Hore, O Franks, L Romano, S Whitelock, L Messam. S Cane, R McCaw (capt).
Replacements: K Mealamu, B Franks, B Retallick, A Thomson, P Weepu, B Barrett, T Ellison.
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