Speaking to reporters in Johannesburg during an ICC top executive visit, Ehsan Mani said there was considerable doubt whether England would tour the embattled Southern African country later this year.
There was "a large body of opinion" within Britain that was opposed to the tour, Mani added. "But it is up to politicians to make moral decisions," he said.
"Our goal is for cricket to flourish and in order for it to flourish the tour must go ahead," he was quoted by the SAPA news agency.
England, Australia and Sri Lanka are scheduled to tour Zimbabwe later this year, but England have delayed confirming their October trip amid strong British Government pressure to scrap the tour in protest at the policies of Zimbabwe President Robert Mugabe.
Crucially, however, the British Government has stopped short of formally ordering the England Cricket Board not to send a team.
Under ICC rules, barring a Government ban, the only other way for the ECB to withdraw without paying compensation is on security grounds. Under new sanctions agreed at an ICC Board meeting in Auckland earlier this month, England risk a two million dollar fine if they fail to tour Zimbabwe.