The New Zealand team is currently scheduled to tour the African nation from next month and cannot cancel without incurring a fine of at least $2 million.
"New Zealand Cricket (NZC) may therefore be forced into a situation of having to tour Zimbabwe even if its members have moral objections to having to play cricket while, just kilometres from the grounds, people are having their homes destroyed and their basic human rights abused," foreign minister Phil Goff said in a letter to the International Cricket Council (ICC).
In the letter released on Wednesday, Goff asked the ICC to exclude Zimbabwe because of its demolition of thousands of shacks and other homes that has left at least 200,000 people homeless.
"The appalling human rights abuses taking place in Zimbabwe cannot be ignored," Goff said.
"We are gravely concerned for the well-being of the people of Zimbabwe, and believe that it is extremely difficult to justify sporting tours going ahead in such circumstances."
He also asked the ICC to change its rules to allow any country to cancel a tour if gross human-rights abuses were occurring in the other country involved.
The request had the overwhelming support of New Zealand parliamentarians and of the Australian government, he added.
At its annual meeting last week, the ICC indicated it did not intend to change its rules to allow the New Zealand tour to Zimbabwe to be cancelled.
NZC chief executive Martin Snedden met Goff on Wednesday and the government confirmed it would refuse to issue visas to the Zimbabwe team for a return tour to New Zealand scheduled in December.