Doug Bracewell, who missed the first two drawn Tests of the series against England in New Zealand this year after cutting his foot on glass then was not selected for the third Test will come into the side.
Former captain Vettori joined the Test squad in England this week after being called up as replacement for spinner Bruce Martin who has been ruled out of the rest of the tour with a calf injury.
Vettori, 34, has not played a Test for 10 months, however, and has been struggling with a long-term Achilles injury.
"Dan is out of tomorrow's game unfortunately. We obviously gave it our best shot but he didn't scrub up that well today and just the confidence to go into a five-day game, with the workload he's had, is just a bridge too far," McCullum said.
"It's disappointing but it does give Dougie the opportunity to make his way back after sitting on the sidelines."
New Zealand lost the first Test at Lord's by 170 runs on Sunday after being skittled out for 68 in their second innings.
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