McCullum, who will retire from international cricket in February, hurt his back in the second ODI against Sri Lanka on Tuesday.
"He's still pretty sore," coach Mike Hesson said after McCullum skipped training on Wednesday.
"It's unlikely he'll play but he's still a chance."
New Zealand won the first two ODIs with ease, and even though they totally outclassed Sri Lanka McCullum was injured when he crashed into the fence in a desperate attempt to cut off a boundary.
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"We don't do things by halves. We're fully committed in the field. If an injury occurs then so be it," he said.
Kane Williamson, who missed the first two ODIs because of a sore knee, is expected to play Thursday and captain the side if McCullum is unavailable.
Hesson said fast bowler Adam Milne, who missed the second game with a troublesome heel, will also play in the next match.
Matt Henry, the chief destroyer in the first two ODIs with two four-wicket hauls, has been rested for the third to make way for returning strike bowler Tim Southee but will return to the squad for the final two games.
Both are returning from injuries and Hesson said all-rounder Anderson would be restricted to batting duties only.