New Zealand Cricket say their summer matches against Scotland and Ireland are "highly unlikely" to go ahead.
The Black Caps are scheduled to play a Twenty20 and a one-day international in Edinburgh on 10 and 12 June.
They are then set to meet Ireland in three T20s at Bready and three ODIs at Stormont, from 19 June to 2 July.
"Clearly, this situation is extremely disappointing for everyone involved in sport," said New Zealand Cricket chief executive David White.
"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."
New Zealand, who had to cut short a visit to Australia after one match, had summer dates in the Netherlands and West Indies too - while they have cancelled a women's tour of Sri Lanka which was due to take place later this month.
Australia are due to play an ODI against Scotland on 29 June before July internationals in England.