A torrential downpour in Wellington meant play never got underway on Thursday and was called just after 1.30pm local time.
The washout leaves Australian captain Healy, who has missed more than a month of cricket, with only two games to prepare for the home Ashes that begin next month.
That could be reduced to one with more rain forecast in the Kiwi capital on Saturday, when the second match of the series is scheduled.
The washout deprives skipper Alyssa Healy of some invaluable match practice ahead of the Ashes. (Darren England/AAP PHOTOS)
Conditions are expected to improve by the third and final game on Monday.
Healy is not expected to keep wicket during the NZ series after flagging she would need more time to fully recover from the injury.
Beth Mooney will take the gloves as she did in the 3-0 series defeat of India earlier this month.
It remains to be seen whether there will be space for both Healy and Georgia Voll in Shelley Nitschke's XI.
Newcomer Georgia Voll has looked right at home in the Australian national team. (Jono Searle/AAP PHOTOS)
As Healy's replacement at the top of the batting order, Voll averaged 86.5 in a stellar debut series against India that earned her a late call-up to the NZ tour.
A knee injury to spinner Sophie Molineux could open up a spot for Voll to shift down the order provided Australia are content carrying Alana King as their only frontline spin option.
Alternatively, Georgia Wareham is the most logical like-for-like replacement for Molineux.
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