With Ross Taylor battling a thigh injury sustained during the one-day series against the touring side, Guptill's inclusion will give New Zealand a extra option across the batting order.
"We opted for extra batting cover for that final spot and with Martin having been playing in the middle-order recently, he can cover a number of positions for us," selector Gavin Larsen said in a statement from New Zealand Cricket.
"Ross is progressing nicely and is expected to take a full part in training tomorrow (Tuesday). The team are looking forward to what will be a special match beginning on Thursday."
The first match in the two-test series at Eden Park will be the maiden day-nighter in New Zealand.
(Reporting by Sudipto Ganguly in Mumbai; editing by Nick Mulvenney)
