St George's School for Girls in Edinburgh, and St Columba's School in Kilmacolm, Inverclyde, are the others.
The Scottish Charity Regulator has ruled that 10 more have passed: the High School of Glasgow, Ardvreck in Crieff, Beaconhurst Grange in Bridge of Allan, Bellhaven Hill in East Lothian, Clifton Hall in Edinburgh, Craigclowan in Perth, Edinburgh Steiner, Kilgraston in Perth, Strathallan in Perthshire and Dollar Academy.
Charity status is regarded as vital by Scotland's private schools because it makes them exempt from VAT and save millions of pounds in costs.
In the case of the three fails, the Regulator's view was that insufficient measures had been taken to provide assistance in respect of high school fees, or to otherwise widen the access to the benefit they provided.
They have all been given 18 months to comply.
The Regulator has been assessing the charitable status of 13 of Scotland's 40 fee-charging schools as a 'priority group' under the test which is defined in the Charities and Trustee Investment (Scotland) Act 2005.
The charity 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'.
Chief Executive David Robb said that the process was ultimately aimed at maintaining public confidence in charitable status by ensuring that Scottish charities met the required standard.
"Charities must provide public benefit, and that is what the legislation requires us to ensure," he said. "While ten of the schools have shown that they do provide a sufficient level of public benefit, we have found that three do not and we have therefore issued them with directions to comply with the legislation passed by the Scottish Parliament.
"As Scotland's guardian of charitable status, we have registered over 5,000 new charities and reviewed dozens more," he added.
"We have produced a large body of reference material to assist charities and our experience is that, even where they charge fees for the services they provide, they can take sufficient steps to widen access and thereby retain charitable status. We look forward to a positive response from these charities as they set out how they intend to address our concerns."
In its report on Fettes College, the Office of the Scottish Charity Regulator (OSCR) said: "After an inquiry, OSCR finds that The Governors of the Fettes Trust (The Fettes Trust), a co-educational independent day and boarding school in Edinburgh, fails the charity test, and has directed the charity to take steps to ensure that it passes the test.
"The fees charged by the charity are substantial and represent a restriction on accessing the majority of the benefit the charity provides.
"Although the charity offers means-tested assistance to those who are unable to pay the full fees, the proportion of its income committed to such assistance (7%) and the number of the school roll who benefit (9.6%) is insufficient to mitigate the level of fees charged by the school.
"The school also provides benefit for which it makes little or no charge. However, the level of such activity and the impact it has is not significant enough to mitigate the school’s fees.
"Under the direction the charity must remove the undue restriction on obtaining the benefit it provides by increasing its spend on means-tested assistance and any other measures as the charity trustees think appropriate to ensure that the charity meets the charity test by 31 July 2014.
"If the charity does not comply with the direction, OSCR will take steps to remove it from the Scottish Charity Register."
Michael Spens, Headmaster of Fettes College, which Mr Blair attended from 1966 to 1971, said: “Although the Regulator acknowledges the valuable public benefit we already provide, they have identified improvements that 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 within the prescribed timescale.”
In its report on St George's School for Girls, the OSCR said: "The fees charged by the charity are substantial and represent a restriction on accessing the majority of the benefit the charity provides.
"Although the charity offers means-tested assistance to those who are unable to pay the full fees, it commits only 4.3% of its income to such assistance. This assistance benefits 12.4% of the main school roll but the charity’s main focus is on lower-value bursaries.
"The charity has not taken sufficient steps to mitigate those fees and therefore OSCR concludes that they are unduly restrictive.
"For these reasons, OSCR finds that the charity does not provide public benefit and it therefore fails the charity test."
Anne Everest, Head of St George’s School for Girls said: “We were very disappointed by OSCR’s decision, given the extensive range of partnerships and work with the community that St George’s undertakes, and which is a matter of public record: our statutory accounts give details of these many activities.
“We were confident in our provision of public benefit when OSCR started assessing us. We shall continue to perform our main charitable function, which is to provide an excellent education for girls. We are committed to providing means-tested bursaries whenever we can, and we shall continue to support education in the community.
“We shall look carefully into OSCR’s report with a view to meeting the public benefit test as soon as possible.
“We are a charity and shall remain a charity. We look forward to having a full discussion with OSCR so that we may decide with them the best way forward.”
The OSCR said in its report on St Columba's School: "OSCR finds that, having had regard to possible unduly restrictive conditions on accessing the benefit provided, the charity does not provide public benefit.
"The fees charged by the charity are substantial and represent a restriction on accessing the majority of the benefit the charity provides.
"The school also provides benefit for which it makes little or no charge. However, much of this activity is relatively infrequent or ad hoc and therefore is not substantial enough to mitigate the level of fees charged by the school.
"The charity has not taken sufficient steps to mitigate those fees and therefore OSCR concludes that they are unduly restrictive.
"For these reasons, OSCR finds that the charity does not provide public benefit and it therefore fails the charity test. "
David Girdwood, rector of St Columba’s School said: "Obviously we are disappointed but not overly surprised.
"St Columba’s as a former girls school has not had a foundation. It is mainly the old boys that create these through financial bequests but we have no history of that.
"We embarked on a programme of bursaries in 2008-2009 and have gone from 0% to 3.5% which we are very pleased about.
"We are pleased too that OSCR recognised the contribution that our staff make to the Scottish education scene and culture and arts. We now intend to increase our 3.5% with a view of satisfying OSCR in 18 months time."
