Tamim was on 36 from 37 deliveries with Bangladesh 39 for one when lunch was taken early because of rain.
New Zealand opted to bowl first with a green wicket, strong winds and overcast skies.
But the only wicket to fall in the first 50 minutes before the rain started was that of Imrul Kayes, out for one, off the bowling of Tim Southee.
Southee was the pick of the New Zealand bowlers with one for six off 5.3 overs, while Trent Boult was expensive with none for 26 off three.