Goff wants the ban in place before New Zealand's scheduled cricket tour in August, on the grounds that cricketers should not be playing in a country with such extensive human rights abuses.
The regime of Zimbabwean President Robert Mugabe has been demolishing homes and razing market stalls in what it calls a bid to to rid the country of squalor and crime. Human rights groups and the opposition have denounced it as a campaign of repression.
About 200,000 Zimbabweans have lost their homes in the blitz, according to the United Nations, but the opposition says the number is closer to 1.5 million.
The New Zealand government does not want the Black Caps to tour Zimbabwe, but has said it will not step in and order them to stay home.
New Zealand Cricket (NZC) says it has an international obligation to tour, and could face a multi-million-dollar fine if it does not.
"The ICC is not considering its responsibilities of a situation where human rights abuses are not simply bad and ongoing but actually have reached an extreme point," Goff told the New Zealand Press Association.
New Zealand would make an approach to the ICC, asking it to waive the fine for forfeiting tours in situations where there were extreme human rights abuses, he said.
Goff said he had also approached British foreign secretary Jack Straw and Australian foreign minister Alexander Downer to see if they would support the proposal.