He experienced back spasms doing warmups and was being treated by support staff, meaning he will not perform in the opener's role.
Instead, first drop Martin Guptill has been promoted to open alongside Tim McIntosh, with McCullum to bat lower in the order.
The tourists awarded a first test cap to fast bowler Andy McKay.
The 30-year-old Wellington left-arm quick's inclusion for seamer Brent Arnel was confirmed shortly before the toss.
Play was delayed for three hours due to a damp outfield at VCA Stadium following a heavy downpour yesterday afternoon.
Officials announced amended hours of play, with two sessions from 1230 (2000 NZT) to 1440 and from 1500 to 1730.
The wicket block itself was fine but one end of the ground was wet and required a substantial amount of sawdust and light rolling as it remained out of the direct sunlight because of the double decker stand that surrounds the 60,000-seat venue.
India made one enforced change, with Ishant Sharma in for injured fast bowler Zaheer Khan.
The series is tied 0-0 after draws at Ahmedabad and Hyderabad.
New Zealand: Daniel Vettori (captain), Brendon McCullum, Tim McIntosh, Martin Guptill, Ross Taylor, Jesse Ryder, Kane Williamson, Gareth Hopkins, Tim Southee, Chris Martin, Andy McKay.
India: MS Dhoni (captain), Virender Sehwag, Gautam Gambhir, Rahul Dravid, Sachin Tendulkar, VVS Laxman, Suresh Raina, Harbhajan Singh, Pragyan Ojha, Shantakumaran Sreesanth, Ishant Sharma.
Match referee: Ranjan Madugalle (Sri Lanka).
Umpires: Simon Taufel (Australia) and Nigel Llong (England).
