Guptill was not named in the 13-man squad for the two-test series after repeatedly failing to showcase his limited-overs form in the five-day version of the game.
He was given a final chance on the recent tour of India but managed only one half century in six innings, continuing his woes against the red ball.
The 30-year-old averages 42.35 in one-dayers but only 29.38 in tests.
His absence means Indian-born batsman Jeet Raval is likely to earn his debut in the first test against Pakistan beginning in Christchurch next Thursday.
Raval was considered unlucky to miss out on the India tour but chief selector Gavin Larsen said he should thrive in New Zealand conditions.
