The umpires made an inspection and decided they would carry out another check at 11:00 am (1000 GMT).
The pitch itself is uncovered and apparently dry but umpires Nigel Llong and Ian Gould said the Edgbaston outfield needed time to dry out.
"It's improving, they have done well, we are going to have another look at 11," said Gould. "It's the whole outfield that's the problem, we have had so much rain. Hopefully we will get some cricket at some stage shortly."
South Africa must win the game if they are to stand a realistic chance of reaching the semi-finals after finally recording their first victory of the tournament, against Afghanistan.
Despite that nine-wicket victory, Faf du Plessis's side are still languishing in eighth spot in the 10-team table after five games, with the top four qualifying for next month's semis.
After Wednesday's game, they will face Pakistan, Sri Lanka and Australia.
New Zealand, by contrast, are flying high and a fourth win would lift the 2015 finalists to the top of the table ahead of matches against West Indies, Pakistan, Australia and hosts England.
Wet weather has caused major disruption at the World Cup, with four no results in which teams shared a point each. —AFP