The top-order batsman damaged the shoulder when fielding in the first test against Sri Lanka in Christchurch and will be sidelined for the next seven to 10 days, almost certainly ruling him out of games two, three and four of the seven-match series.
"Kane is obviously a very important player for us and we need to give his shoulder the time to fully recover," New Zealand coach Mike Hesson said in a news release.
"He's played a lot of cricket of late and this window will allow him to get back to 100 percent."
New Zealand co-host the World Cup with Australia from Feb. 13 to March 29.
(Reporting by Nick Mulvenney in Sydney, editing by Sudipto Ganguly)
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