Kane Williamson is out of today's New Zealand XI game against Ireland in Hamilton and the first South African match.
He damaged his left wrist during Northern Districts' trip to the Champions League in India last month.
He will be reassessed early next week with a view to getting him involved at a later point in the series.
Seamer Tim Southee is expected to be fit for next Tuesday after having a shoulder problem.
It all adds up to a slightly messy start to the biggest summer for New Zealand cricket in 22 years.
A group of 13 was named yesterday for the second NZ XI game of the week - after a squeaky one-run win over Scotland at Lincoln on Wednesday.
Captain Brendon McCullum is sitting the match out, but wicketkeeper BJ Watling, allrounder Jimmy Neesham and swing bowler Trent Boult are in the 13.
The Scottish game served a useful purpose. It could easily have been lost, a result that would have brought considerable embarrassment.
But as an early wakeup call, it was a good exercise.
Ireland, who have caused World Cup shocks before - beating Pakistan in Jamaica in 2007 and England in Bangalore three years ago - got their New Zealand trip off to a scratchy start, losing by three wickets to Northern Districts on Thursday, mustering only 153 against a less than full-strength ND attack.
For Ireland and Scotland, who played Canterbury yesterday in Christchurch, the cup warm-up visits are important to get a feel for what to expect next February.
Afghanistan had four games in New Zealand earlier in the month. United Arab Emirates are the other associate member country coming to the World Cup.
Due respect to the major nations, but the game needs these four countries to step up at the tournament.
There have been boilovers at past tournaments.
Ireland's Kevin O'Brien made his name when he hammered the fastest World Cup century, 113 off 63 balls to help chase down 327 against England for a three-wicket win at Bangalore.
Alex Cusack was in the team which beat England.at Bangalore. Brisbane-born but a professional in Ireland for several years and married to a Dubliner, he's well placed to assess the target for the four associates.
"It's a great opportunity for all the associates to do well against the bigger teams and hopefully try and get a couple of wins," he said.
"Every time the Irish team plays in the World Cup we're looking to do really well and keep putting our name up in the spotlight.
"In doing that, we're working together with the other associates to try to bridge the gap."
New Zealand XI
Squad to play Ireland in Hamilton today:
Martin Guptill, Tom Latham, Dean Brownlie, Corey Anderson, Jimmy Neesham, Luke Ronchi, BJ Watling, Dan Vettori, Nathan McCullum, Kyle Mills, Matt Henry, Mitchell McClenaghan, Trent Boult.
