Johann Lamont said that it was "not viable" to fund a mass-participation university system using only public funds.
Speaking on 17 December at an address in Glasgow marking one year as leader, she said that Scotland had to "look at whether current higher education funding arrangements are fair".
"While it is undoubtedly true that higher education is a public good, it also results in private gain to those who undertake it. Graduates not only receive higher lifetime returns, but a disproportionate number also come from more privileged backgrounds," she said.
"These two points, taken together, mean that a no-charge system is essentially regressive."
However, she said that Scottish Labour would not support up-front fees "because people perceive that as a barrier".
Scottish-domiciled students attend university in the country for free, although have to pay up to £9,000 to study elsewhere in the UK. Students from England, Wales and Northern Ireland are also charged up to £9,000 to study in Scotland. Because of European equality rules, European Union students also study for free in Scotland.
"Is £75 million a year [to subsidise] European students a price worth paying to keep a no-tuition fee policy for Scottish students while our colleges are under attack?" Ms Lamont asked.
She also painted a picture of decline for the Scottish academy's future. "We need a long-term solution to higher education funding in Scotland. If we do not find one, Scottish universities will begin to lose ground against their international competitors," she predicted.
Referring to the Times Higher Education World University Rankings 2012-2013, she added: "This autumn, it was reported that Scotland's top universities, including St Andrews, Aberdeen and Glasgow, had fallen down an international league table. The international reputation for Scottish higher education is at risk."
In a separate development, the Scottish government announced yesterday that there would be an extra 2,000 student places available in 2013, including 700 reserved for students from disadvantaged backgrounds.