After New Zealand had won the toss and elected to field, the rain started and the covers were put in place.
It cleared sufficiently to allow an umpires' inspection at 3.10 p.m. after which it was announced that a 24 overs match would start at 3.45.
New Zealand selected all-rounder Corey Anderson, who was added to the squad in place of the injured Grant Elliott. Anderson replaced pace bowler Tim Southee, who has an ankle injury.
Off-spinner James Tredwell came into the England side in place of Graeme Swann, who has a calf strain.
The winners will advance to this week's semi-finals.