Tuesday's game in Mount Maunganui will be the third McCullum has missed since he was injured on December 28 while fielding against Sri Lanka in the second game of the five-match series.
Coach Mike Hesson initially said McCullum, who will retire from international cricket after next month's Tests against Australia, had a chance of completing the Sri Lanka series.
McCullum backs Amir's return to Pakistan squad
But Hesson said on Monday that the skipper will not be considered until the first ODI against Pakistan in Wellington on January 25.
"He's really struggling," said Hesson. "He hasn't progressed as well as we'd thought. He will get a further assessment."
McCullum had already announced he would sit out the Twenty20 matches against Sri Lanka and Pakistan as he will not be going to the World Cup in March.
Fast bowler Tim Southee, who suffered a foot injury in the third ODI against Sri Lanka in Nelson last Thursday, will also miss Tuesday's game.
However, his regular new-ball partner Trent Boult returns to the side after being rested for the first four games.
With New Zealand 2-1 up, Sri Lanka need to win on Tuesday to draw the series after earlier being beaten 2-0 in the Tests. The fourth ODI was abandoned Saturday because of heavy rain.
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