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The Crusaders and All Blacks great was set to make his debut for the franchise against the Hurricanes last weekend before suffering a calf strain at training on Thursday.
It seems he won't be taking the field this Sunday against the Chiefs either.
Carter didn't take part in Blues training today, sticking to gym duties instead.
Newstalk ZB Sport understands he is targeting next weekend's match against the Highlanders in Dunedin.
Blues first five-eighth Otere Black took part in some training today after suffering a neck injury in the defeat in Wellington on Saturday.