The 2012 World Player of the Year sustained the injury playing for the Canterbury Crusaders in their Super Rugby victory over the New South Wales Waratahs at the weekend and a decision on his availability will be made later in the week.
Aaron Cruden is most likely to replace Carter should he be ruled out the test at Eden Park after some fine performances for the Waikato Chiefs this year and Wellington Hurricane Beauden Barrett, a solid place-kicker, also in the squad.
"It's only a crack, it's not completely broken, not displaced," All Blacks coach Steve Hansen told local media.
"We'll see how the swelling goes and make a decision on that late in the week... We're very fortunate we've got people like Crudes and Barrett available."
Props Tony Woodcock, Owen Franks and Ben Afeaki were also carrying injuries, the NZRU said, so uncapped Crusaders loosehead Joe Moody has been called into the squad as cover.
Moody's inclusion in the 32-man squad along with Charles Piutau, Francis Saili, Steven Luatua, Afeaki, Jeremy Thrush and Matt Todd brings the total of uncapped players to seven.
Flanker Todd was listed as an 'injury replacement' in the original squad because Sam Whitelock has a broken finger and will miss the first two tests but is expected to be fit for the third on June 22 in New Plymouth.
Scrumhalf Piri Weepu was knocked out in the Auckland Blues' defeat to the Otago Highlanders on Saturday in Dunedin, lying prone on the ground for several minutes before receiving treatment.
"Piri Weepu is suffering no side effects of his concussion from the weekend but will be limited to non-contact training until he is reviewed later in the week," the NZRU news release said.