The Blacks Caps then host India for three One-Day Internationals (ODI) in Auckland, Hamilton and Christchurch.
Both sides are looking to bounce back after being knocked out of last week's semi-finals of the ICC Twenty20 World Cup.
India have rested stars Rohit Sharma and Virat Kohli for the New Zealand tour while head coach Rahul Dravid also sits out, with VVS Laxman, head of India's National Cricket Academy, in charge.
Suryakumar Yadav, India's new batting sensation, and pace bowler Umran Malik are included in the India squad.
All-rounder Hardik Pandya captains the T20 side with Shikhar Dhawan taking over as skipper for the ODIs.