New Zealand Cricket conceded upcoming tours to Europe and the West Indies were unlikely to proceed Friday, with doubts also hanging over a planned visit to Bangladesh.
NZC chief executive David White said the trips to Ireland, Scotland, the Netherlands and the Caribbean scheduled for June-July were "most unlikely", while there were "obvious question marks" about touring Bangladesh in August.
"Clearly, this situation is extremely disappointing for everyone involved in sport but, given the bigger picture, and the terrible toll COVID-19 is taking worldwide, we need to look after not only our own people but the greater community good," White said.
He confirmed this month's tour to Sri Lanka by the White Ferns women's team had been cancelled.
All cricket has been stopped as New Zealand undergoes a four-week COVID-19 lockdown and White said NZC was examining possible playing scenarios for next season.
"Our current focus is very much on ensuring the future sustainability of cricket in New Zealand," White said.