Stuart Ramsay's exit was confirmed after the board met yesterday to discuss a report by investigators Kroll into newspaper reports that former chief executive Euan Sutherland had been in line to be paid £3.6 million before he quit in March.
There had also been concern about how a report by former City Minister Lord Myners into the bank's corporate governance reforms became public.
The Co-operative Group said: "Following an independent report, and at the request of the board, Stuart Ramsay has left the board of the Co-operative Group with immediate effect."
A source familiar with the situation said the Kroll investigation had revealed "there had been some dissemination of confidential board material".
Today, a separate independent report by Sir Christopher Kelly, into the Co-operative Bank's near-collapse after its takeover of the Britannia Building Society in 2009, is due to be published.
Sir Christopher is expected to be critical of former executives and board members after the bank was left with a £1.5 billion hole in its finances.
It was previously thought that Mr Ramsay, who is chairman of the Scottish board of the Co-operative, had retired and had not stood for re-election.
In March, details of Mr Sutherland's salary and other payments were published by a Sunday newspaper. The report also contained information about six other directors' salaries and retention fees, along with those of financial director Richard Pennycock.
Mr Sutherland was incensed, saying at the time: "We have an individual, or individuals, determined to undermine me personally, my team and the rest of the group board."
He stepped aside shortly afterwards, claiming his attempts to reform the mutually owned company and take it in a more commercial direction were being frustrated by some insiders.