John Edward, director of the Scottish Council of Independent Schools, said schools will "adapt practice accordingly in a way that best suits the pupils and matches regulatory requirements".
It comes after MSPs passed the controversial Gender Recognition Reform (Scotland) Bill last month following intense debate in the Scottish Parliament.
The legislation will make it easier for transgender Scots to obtain a gender recognition certificate, and also lowers the minimum age for applicants from 18 to 16.
Shona Robison, the SNP social justice secretary, said 16-year-olds can leave home, marry and vote and the change would align with this, but critics called it “worryingly misguided”.
There are six mainstream single-sex private schools in Scotland. Two of them, The Mary Erskine School and Stewart’s Melville College in Edinburgh, are “closely twinned”. They see boys and girls taught together from nursery to Primary 7, before separating and joining together again in a “co-educational sixth form”.
Others offer single-sex education throughout, such as St Margaret’s School for Girls in Aberdeen. Merchiston Castle School in Edinburgh takes boys between the ages of seven and 18.
Mr Edward said schools have been “well aware of the range of issues related to gender identity that manifest among their pupils for some time – from gender neutral policies to individual pastoral support”.
He said: “All schools – whether single-sex or co-ed – will act appropriately, according to the identity of the pupils as indicated and their wishes in education.”
Mr Edward added: "If a pupil is no longer the same gender as a single-sex school, then that is something the school and the pupil would work through, but no-one is making hard and fast rules now, they will adapt practice accordingly in a way that best suits the pupils and matches regulatory requirements.”
The new legislation passed by a margin of 86 votes to 39 in Holyrood following days of intense debate and numerous attempted amendments.
Nine SNP MSPs, including former minister Ash Regan, defied the party whip. Labour’s Carol Mochan and Claire Baker did the same, with both resigning from their frontbench positions.
Tory MSP Rachael Hamilton had pushed an amendment seeking to limit applications to those over 18.
She said: “In Scotland, an individual under the age of 18 is not considered old enough to stand for election in this Parliament, nor can they serve as a juror, place a bet, buy or sell alcohol, get a tattoo or be permitted to watch certain films at the cinema. As with obtaining a gender recognition certificate, I would agree that there is good reason for this.”
Ms Robison said the issue of age had been “one of the most difficult to address”. However, she said: "Young people in Scotland are empowered at 16 to leave home without parental consent, to get a full-time job, pay national insurance, enter into a legally binding contract, consent to medical procedures, to marry, change their name, and vote for members of this parliament.”
Ms Hamilton’s amendment was defeated by 87 votes to 37.