New Zealand, one of the favourites to win the World Cup they are co-hosting with Australia, were struggling at the time, having slumped to 157 for seven when the weather halted play.
Zimbabwe were set a revised target of 156 off 30 overs to win but the match was called off before the Africans could commence their reply.
New Zealand opener Martin Guptill blasted an even 100 for the home team off 86 balls, featuring 13 boundaries and two sixes, but got little help from his team mates with only Ross Taylor (11) making double figures.
Tinashe Panyangara and Elton Chigumbura both captured two wickets each for Zimbabwe, one of the rank outsiders for the World Cup.
New Zealand will play their final warm-up against South Africa in Christchurch on Wednesday, while Zimbabwe will face Sri Lanka the same day.
The World Cup starts on Feb. 14 when New Zealand meet Sri Lanka and Australia face England in Melbourne.
(Reporting by Julian Linden in Singapore. Editing by Patrick Johnston)
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