The five-week tour is set to start in August and the leader of a minor party in the coalition government has already written to the players urging them to pull out.
Clark told radio Newstalk ZB that in deciding whether a tour should go ahead New Zealand Cricket (NZC) usually assessed the issue on security reasons, rather than political ones.
"I have to say that, if it were me, I would not be going on either ground," she said.
"Zimbabwe has just had elections that no reasonable person would agree were free or fair."
President Robert Mugabe, who has been in power since Zimbabwe's independence from Britain in 1980, won a sweeping victory in the March 31 election, but foreign critics led by the United States and the European Union dismissed the poll as a sham.
New Zealand captain Stephen Fleming said he had yet to see the letter from Green Party leader Rod Donald, but was confident the issue would be suitably dealt with by NZC chief executive Martin Snedden.
New Zealand's last tour of Zimbabwe in 2000 was given the go-ahead by Snedden's predecessor, Chris Doig.
However, Snedden refused to let the New Zealand team travel to Kenya for a match during the 2003 World Cup because of terrorism fears.
A tour of Pakistan later that year was delayed after e-mailed threats were received about touring during the holy month of Ramadan.
Last year, England's tour of Zimbabwe was in doubt after Zimbabwean authorities imposed a media ban on 13 British journalists.
After a two-day delay, England's cricketers finally flew out when the ban was lifted, but cut short their itinerary.