Peever, who was recently reelected for another three-year term, will be replaced by deputy chairman Earl Eddings for the interim period until a permanent appointment can be made, CA said in a statement.
Peever had come under heavy pressure following CA's delayed release of the independent Longstaff report on Monday, which described the board as "arrogant" and "controlling", and of nurturing a culture of "winning without counting the costs". .
Eddings thanked Peever for his service.
"He has played a pivotal role in the elevation of women’s cricket, and the significant growth in attendance and participation," he said in the statement.
“The board is keenly aware that we have a way to go to earn back the trust of the cricket community. We and the executive team are determined to make cricket stronger."
The Longstaff report blamed CA in part for the ball-tampering scandal in Cape Town in March that led to long suspensions for the test side's former captain Steve Smith, and batsmen David Warner and Cameron Bancroft.
CA delayed releasing the report until after Peever was reelected at an annual general meeting last week, prompting heavy criticism from luminaries including former board boss Malcolm Speed and former Australia Prime Minister Kevin Rudd.
Peever, who succeeded Wally Edwards in 2015, had tried to ride out the storm with a string of media interviews on Monday and described the ball-tampering incident as a "hiccup".
But the CA leadership's refusal to be accountable for the findings in the review, having issued heavy punishments in the ball-tampering scandal, angered former players and pundits.
Former Australia captain Ian Chappell said CA had become "a joke", while a governance expert who helped remodel the board into its modern entity described Peever's reelection only days before the review's release as "astonishing".
At least three of Australia's state cricket associations have declined to endorse Peever's leadership since the review's release on Monday, local media reported.
Former Australia captain Mark Taylor, a CA board director, will be backed to take over from Eddings, having already been endorsed by a number of prominent cricket figures.
(Reporting by Ian Ransom; Editing by Peter Rutherford)
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