Families were told last night that Fernhill, a co-educational school on the outskirts of Glasgow, had called in administrators after entering financial difficulties and could shut this month unless a rescue package is put in place.
It is understood the school in Rutherglen, South Lanarkshire, is blaming falling school rolls and a decline in fee income for the situation.
There are some 230 pupils and about 40 staff at Fernhill, which was a single sex girls' school until last year when it announced it was going co-educational.
The news was delivered to parents at a meeting. Some were too upset to speak as they left, while others said it was the "end of an era".
One woman with children at the school said: "It was an emotional meeting. The school board are trying to work something out but it was a bit of a gabble and people need to calm down. They told us that administrators had been contacted but have not been appointed.
"I feel sorry for the board members because they tried their best to keep the school open. They offered that anybody who could provide finance could just take the school and run it. We're devastated. It's a fabulous school."
Another parent added: "It is very sad. There were parents at the meeting who were pupils there themselves. We'll have to look for other schools for our children now. If there was a chance Fernhill could stay open everybody would stay here."
The school is expected to stay open until the end of the current term and the start of the summer holidays. One father with two children at Fernhill said that there was no anger directed towards the governors over the threat to close.
He said: "There was frustration, but no anger. There's no suggestion of financial mismanagement, just the problems that came to many businesses during the recession of the last five years."
However, another parent contacted The Herald to question the way the school had been run.
He said: "It doesn't seem to be that difficult. You count up the income you get in fees and then cut your costs accordingly.
"I don't know why the owners have not cut costs before getting to this stage if the pupil numbers were dropping.
"This is one of the best independent schools in Scotland and it is terrible that it looks as if it has to close."
An indication of the difficulties facing Fernhill first surfaced in 2011 when the governors took a decision to freeze the fees for two years.
But last year, the fees were raised above the level of inflation and are now £9300-a-year for a senior day pupil.
In 2013 the school also introduced a plan to allow families to spread the cost of fees over 10 years to make it more affordable. At the time, Tony Boswell, chairman of the school board, said: "We recognise that times are tough and we have been striving to develop a solution that helps families who may otherwise be unable to afford an independent education."
Fernhill began as a primary for girls in 1953 run by the Sisters of Notre Dame and was earmarked for closure in 1971.
A committee of parents was formed to save the school and the current establishment reopened the following year. A secondary department was opened in 1973.
The school stands in some nine acres of wooded grounds on the outskirts of Glasgow close to the Cathkin Braes.
Plans to make the school fully co-educational were announced in 2013.
The last Scottish private school to close after hitting financial difficulties was St Margaret's in Edinburgh, which was founded in 1890. The school called in the receivers in 2010.
The threatened closure comes at a time when the number of pupils enrolling in independent schools in Scotland has been falling due to the impact of the recession, with a 3% decline since 2007.
Numbers enrolling in primary have dropped by 7%.
Others who contacted The Herald said families knew nothing about the proposed closure until a meeting yesterday evening.
One said: "The email telling us about the meeting seemed to suggest there was a way forward for the school, but my daughter texted me this afternoon saying it was going to close.
"It was a terrible shock because this is such a close-knit school community. We can't understand what has happened and we don't feel we have been told about the true situation.
"It seems the staff members were told last week and those with children were trying to get them into different schools, but we were left in the dark."
The school was unavailable for comment.