Brian Boyd, emeritus professor of education at Strathclyde University, in Glasgow, said the suggestion was "misconceived" and "out of kilter" with the notion of a Common Weal.
The attack came after another prominent Scottish academic published a paper, commissioned by the Scottish Government, on whether greater use could be made of private money in education.
Lindsay Paterson, Professor of Education at Edinburgh University, suggested the setting up of a National Lottery-style fund to which state and private schools could bid for bursaries on behalf of pupils excelling in disciplines such as music, dance, sport, languages, mathematics, science, writing and leadership.
The proposal also covers donors of larger sums of money who would be allowed to fund particular schemes directly.
Professor Paterson said the ultimate purpose was a change to Scotland's educational culture so that it would have the reputation "not only of providing opportunities for everyone, but, also, once more, of fostering true individual excellence."
However Professor Boyd said there were far better ways of using philanthropic money than on "elitist schemes" to benefit a minority of pupils, adding: "There is no place for vanity projects in our education system."
Eileen Prior, executive director of the Scottish Parent Teacher Council, said families were also likely to have strong views about the purpose of such giving.
"Commercial involvement in schools is a difficult and emotive area because not every parent will agree with the nature of the business or the benefits the companies look for," she said.
"It seems likely that philanthropy in schools is likely to touch some of the same issues.
"This is not charitable, anonymous giving - it is funding for specific projects or activities and, as such, we imagine parents will have strong views about the source of any funding, its purpose and the influence such funders are likely to expect in return."
However, Liz Smith, education spokeswoman for the Scottish Conservatives, said: "The paper is both radical and timely.
"It correctly identifies that success in Scottish schools, whether in the private or public sectors, owes much to several generations of philanthropists."