The call comes after three Scottish independent schools – including Fettes College, in Edinburgh – were told they had failed the public benefit test required of all charities.
The Scottish Charity Regulator ruled Fettes, St George's School for Girls in Edinburgh, which charges more than £11,000 a year, and St Columba's School in Kilmacolm, Inverclyde, which charges nearly £10,000 a year, did not do enough to offset their fees.
Fettes, which former prime minister Tony Blair attended from 1966 to 1971, charges annual fees of up to £28,000 for boarders, but spends just 7% of its income on financial support.
Ten private schools passed the public benefit test, including the High School of Glasgow, Beaconhurst Grange in Bridge of Allan, Clifton Hall in Edinburgh, Kilgraston in Perth, Strathallan in Perthshire, and Dollar Academy.
Those that failed have 18 months to comply with the ruling before they face being struck off the charities register.
Hugh Henry, education spokesman for the Scottish Labour Party, said: "It is not acceptable that these schools are failing to demonstrate public benefit despite receiving the financial support of having charitable status.
"If they cannot or will not show they are providing the public benefit which the legislation requires, then the regulator must act to remove their charitable status."
The status is seen as vital by private schools because it makes them exempt from VAT, saving them millions of pounds.
The regulator has been assessing the charitable status of the schools under the test defined in the Charities and Trustee Investment (Scotland) Act 2005.
The test sets the standard that all charities must meet in providing public benefit. Where there are conditions on the public gaining access to the benefit, such as fees or charges, charities must take steps to ensure these are not "unduly restrictive".
In the case of the three schools that failed the public benefit test, the regulator ruled insufficient measures had been taken to provide assistance to offset the high fees charged.
David Robb, chief executive of the Office of the Scottish Charities Regulator (OSCR), said the process was aimed at maintaining public confidence in charitable status.
"While 10 of the schools have shown that they do provide a sufficient level of public benefit, we have found that three do not and have therefore issued them with directions to comply," he said. "Our experience is that, even where they charge fees, they can take sufficient steps to widen access and thereby retain charitable status."
Fettes headmaster Michael Spens said: "Although the regulator acknowledges the valuable public benefit we already provide, they have identified improvements they wish to see implemented.
"We are naturally disappointed by this outcome but strongly believe that, by working with OSCR, we can satisfy the requirements of their charities test."
Anne Everest, the head of St George's, also expressed disappointment and highlighted the school's "extensive range of partnerships and community work".
She said: "We were confident in our provision of public benefit when OSCR started assessing us. We are committed to providing means-tested bursaries whenever we can, and we shall continue to support education in the community."
David Girdwood, rector of St Columba's, said the school had no financial foundation created by bequests. "We embarked on a programme of bursaries in 2008/09 and have gone from 0% to 3.5% which we are very pleased about," he said. "We are pleased OSCR recognised the contribution our staff make to the Scottish education scene and culture and arts and we now intend to increase our 3.5%."