The wicket-keeper batsman suffered a fractured finger in a warm-up game but will still travel to England this week ahead of the tournament.
Tom Latham, the New Zealand wicket-keeper, faces a race against time to be fit for his country's World Cup opener against Sri Lanka on June 1.
The 27-year-old suffered a fractured finger during the third warm-up match against an Australia XI in Brisbane last week.
Latham was in immediate discomfort upon taking the blow and was removed from the field for further assessment.
An X-ray has since revealed the full extent of the injury but he will travel with his Kiwi teammates to England on Sunday.
News of the injury comes just over two weeks before the Black Caps' opening match in Cardiff at the start of next month.
Uncapped 'keeper Tom Blundell is likely to step-in if Latham is ruled out for a sustained period. New Zealand are permitted to tinker with their 15-man squad until May 23.
"I was just keeping to Matt Henry – a ball down the legside, I dived for it and didn't quite get it in the gloves properly," said the Christchurch-born player, who has played 85 ODIs for his country.
"I kept keeping for a few overs, then I took my glove off and my finger wasn't quite in the right direction – very disappointing but the good thing is I should be okay.
"This week and next week are going to be pretty important in terms of recovery – once we get over there we'll certainly start to progress things in holding a bat and catching balls. Certainly, this isn't ideal timing.
"It's just about making sure the bone starts to heal. It's hard to put a timeframe on it until we start catching balls with the gloves on, then we should start to know more. It's a bit of a waiting game at the moment.
"But it's certainly feeling better and better each day, which is a positive sign."
Our coverage of the ICC Cricket World Cup 2019 is brought to you in association with Cricket 19, the official video game of the Ashes. Pre-order your copy now at Amazon.co.uk
Welcome to www.thecricketer.com - the online home of the world’s oldest cricket magazine. Breaking news, interviews, opinion and cricket goodness from every corner of our beautiful sport, from village green to national arena.