Olonga fled Zimbabwe in 2003 after wearing a black armband during a World Cup match to mourn what he called the death of democracy in his country.
Donald said he would take Olonga on a speaking tour to "turn up the heat" on the government.
"We want Henry to give the government, New Zealand Cricket (NZC) and the people, the message loud and clear that the Black Caps should not be touring Zimbabwe," he said on Sunday.
"The Government should be doing everything in its power to get the Black Caps off the hook, and needs to match its tough talk with decisive action."
The government's position is that it does not want the team to tour, but will not stop it because that would need legislation authorising the removal of passports.
Foreign minister Phil Goff last week announced a diplomatic offensive against all sporting contacts with Zimbabwe, and is urging the International Cricket Council (ICC) to waive financial penalties that would be imposed if the tour does not go ahead.
Goff has said the government will refuse to issue visas to the Zimbabwe team for a return tour to New Zealand scheduled in December.
NZC's chief executive Martin Snedden said his association has no alternative but to go on tour or face crippling fines believed to be at least $2 million.
Donald drafted a bill that would allow the government to stop the tour, but it has been vetoed on the grounds that it would cut across New Zealand's human rights laws.
"We hope Henry's visit will lead to public pressure increasing on the Government to stop the tour," he said.
The Greens are bringing Olonga to New Zealand, and he will speak at public meetings in Christchurch, Wellington and Auckland this week.
President Mugabe's order to destroy thousands of homes and businesses triggered the Green's protest.
The demolitions campaign has left between 200,000 and 1.5 million people homeless according to the United Nations and the Zimbabwe the opposition respectively.