Smith scored the match-winning try in New Zealand’s first-Test victory at Auckland’s Eden Park, but was injured last weekend as the All Blacks sealed a series triumph with a 28-27 success in Dunedin.
The world champions were hopeful that Smith had avoided a fracture to his thumb.
However, that has not proven to be the case and the 32-year-old is now facing five to six weeks on the sidelines, meaning Malakai Fekitoa or Ryan Crotty is set to step in.
New Zealand coach Steve Hansen said at a press conference: “What we thought was only a muscle injury has turned out to be a broken bone for Conrad Smith in his thumb, so he won’t be considered for Saturday unfortunately.
“It’s bad luck for him and an opportunity for someone else.
“We have an idea of who we’ll go for, but we don’t need to tell England who that is.
“Ryan’s been there and done that and been in the atmosphere, but what it’ll come down to is whether we think Malakai’s ready or not.”
Tongan-born Highlanders back Fekitoa, 22, made his international debut as a replacement in the first Test against England, while 25-year-old Crotty boasts five caps.
New Zealand will name their team on Wednesday, with number eight Kieran Read expected to return following a spell on the sidelines due to concussion.
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