Eric Milligan, whose commission on poverty led to the creation of the One City Trust, said councillors were to blame for its demise.
He accused the Liberal Democrat-SNP administration running the city of a lack of compassion over social exclusion for its decision to withdraw support for the charity, which for the last five years has funded initiatives in the most deprived parts of Edinburgh.
He said the downgrading of the charity, understood to be surviving on donations from businesses and trust funds, is symptomatic of a wider attitude, reflected in the council's moves to close schools in deprived areas.
It emerged at the weekend that the charity – backed by celebrities including Ian Rankin, Gordon Strachan, JK Rowling and Irvine Welsh – was facing being wound up after losing its funding from the council.
It has been left without any staff and no major projects to work on. The council has blamed the economic downturn for its withdrawal of 35,000 in funding.
The charity was launched in 2004 after a study found that one in five children in the city were being raised in poverty.
The creation of the One City Trust was a key recommendation of the 100,000 study, which was chaired by then-Bishop of Edinburgh Richard Holloway.
Among the most successful projects were a collection of short stories by Irvine Welsh, Ian Rankin and Alexander McCall Smith.
Councillor Milligan told The Scotsman: "I don't know of anything the current administration has done to support it. It is a lot less interested in these kind of issues than we were.
"You only have to look at some of its recent decisions, such as the recent school closures, to see that. If you allow things to slide like they have done, they will simply wither away and die.
"There is a wider issue here that the city doesn't appear to be doing very much any more. Edinburgh is in danger of being synonymous with inactivity, with councillors sitting agonising over everything. They are in danger of becoming constipated."
Council leader Jenny Dawe denied suggestions she had been working behind the scenes to try to get a new pet charity for the council off the ground. But she told The Scotsman that she felt One City had been run "atrociously" and had "lost sight" of what it was set up for.
"The problem was it ended up falling between a council body and an external organisation. Some very bad decisions were taken," she said.
The current chair of One City's board, Harry O'Donnell, said: "We have to hope there is a corporate maturity about this."
ERIC Milligan's special commission on social exclusion was launched in October 1998 to find practical ways to allow all of the capital's citizens to benefit from the city's growing prosperity.
A total of 14 representatives from business, charities, universities and churches were appointed to sit on the commission. Its final report, which was published in June 2000, painted a picture of a sharply divided city and warned that unless measures to improve areas such as childcare, housing and health are introduced, the gap between the haves and have-nots in the capital would widen.
But it took another four years to get the charity up and running, shortly before the launch of the first major project.