Any cancelled pool games are deemed 0-0 draws. Rules set before the tournament left no room for the provision to postpone pool games.
The All Blacks and Italy would, therefore, share two points each. That would see the All Blacks finish top of Pool B, one point ahead of South Africa who they defeated in their opening match.
In this scenario, Italy would remain third in the pool and miss the knockouts.
At this stage it is unclear who the All Blacks will face in the quarter-finals.
World Cup organisers are hopeful Scotland and Japan in Yokohama will still go ahead while Ireland face Samoa in Fukuoka on Saturday.
England's match against France, scheduled for Saturday in Yokohama, has also be cancelled. That's likely to see England take on Australia and France meet Wales in their respective quarter-finals.