He drew attention to concerns voiced by the Scottish Council of Voluntary Organisations that the decision undermined the public perception of charities.
The one-time Edinburgh education convener told MSPs: "Private schools are bastions of privilege which help to perpetuate class division."
But his comments in the Scottish Parliament prompted a counter-attack by SNP minister Fergus Ewing on Lord Foulkes' own education at a private school in Hertfordshire.
After pointing out the charities legislation set a "public interest" test which some private schools passed and some did not, Mr Ewing continued: "I note that Lord Foulkes did himself attend Haberdashers' Aske's, a notable private school.
Those who benefit from a particular system should perhaps not decry others from having the opportunity so to do."
But Lord Foulkes challenged presiding officer Alex Fergusson: "If we take what the minister suggests, doesn't both he and you have to declare an interest also?"
Mr Fergusson is an old Etonian and Mr Ewing went to Loretto private school, near Musselburgh.