The announcment was further proof of the problems posed to world cricket by the troubled African state, now dealing with the fall-out from a disputed presidential election.
In a statement issued from its Dubai headquarters, the ICC's British president-elect, David Morgan, said there had been a "fundamental breakdown" between Australian Speed and a number of board members, including current ICC president Ray Mali of South Africa.
"This change of plan is the result of a fundamental breakdown in the relationship between the CEO and a number of Board Members, including the President, over a variety of issues that include Zimbabwe," Morgan said.
Speed will go on paid leave from April 30 until the end of his contract term on July 4.
David Richardson, the ICC's general manager, will serve as interim chief executive until the former South Africa keeper's compatriot Haroon Lorgat takes over as planned as chief executive at the ICC's annual conference in July.
The extraordinary development is understood to have been prompted by Speed's unhappiness at the ICC board's failure, following its March meeting, to take any significant action against Zimbabwe Cricket (ZC) after an independent forensic audit carried out by leading accountants KPMG raised questions about the state of ZC's finances.
After that meeting, Speed, ICC chief executive since 2001, refused to attend a media conference, saying he was not prepared to defend in public a decision with which he fundamentally disagreed.
In July last year, a confidential report co-written by Speed, a lawyer by profession, containing several withering criticisms of ZC's finances was leaked.
"It is clear that the accounts of ZC have been deliberately falsified to mask various illegal transactions from the auditors and the government of Zimbabwe," Speed said in the report.
It is now expected that, for the first time in its 99 year-history, the ICC's annual conference will not be held at Lord's but in Dubai.
That move has been prompted by doubts over whether Peter Chingoka, the ZC chairman, would be admitted to Britain to attend the conference.
England's hosting of next year's ICC World Twenty20 has been threatened by the British government's hardline opposition to the regime of the country's current president Robert Mugabe and his ZANU-PF party.
Zimbabwe have been in decline as an international cricket force since a race row in 2005 led to the dismissal of former captain Heath Streak.