After a 20-minute rain delay at the start, only nine overs were possible before the rain returned and the umpires took the players from the field with New Zealand 102 for four.
Colin Munro blasted a whirlwind 66 off 23 deliveries after the West Indies won the toss and put New Zealand into bat.
Munro equalled his own New Zealand record when he reached his half-century off 18 deliveries.
His rollicking knock included 11 fours, three sixes, and just two singles and a two.
New Zealand remain 1-0 up in the series with the third and final match at Mount Maunganui on Wednesday.