Bairstow has been drafted into the line-up as cover for the injured Joe Denly, who was earlier ruled out of the T20Is due to an ankle injury.
Denly damaged his right ankle ligaments while training a couple of weeks ago and is unlikely to play in the first red-ball warm-up game for the tourists.
The 33-year-old, who impressed with resolute performances during the Ashes, was spotted in the nets on Thursday but England have opted for cautionary measures by roping in Bairstow.
The 69-Test wicketkeeper-batsman endured an ordinary Test summer, averaging 19.45 across six matches including a pair of ducks against Ireland at Lord's.
England's national selector Ed Smith had asked the doughty batsman to stage a strong comeback to the longer format following his mediocre outings.
Bairstow played three of the four T20I games in New Zealand and will remain with the squad after the completion of the limited-overs fixtures.
The first Test between the two sides will commence on November 21 in Tauranga.
Joe Root (c), Jofra Archer, Jonny Bairstow, Stuart Broad, Rory Burns, Jos Buttler, Zak Crawley, Sam Curran, Joe Denly, Jack Leach, Saqib Mahmood, Matthew Parkinson, Ollie Pope, Dominic Sibley, Ben Stokes, Chris Woakes