Families were told last night that Fernhill, a co-educational school on the outskirts of Glasgow, had contacted 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 rolls and a decline in fee income for the situation.
There are 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."
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 term and the start of the summer holidays.
An indication of the difficulties facing Fernhill first surfaced in 2011 when the governors froze fees for two years. Last year, fees were raised above the inflation level and are now £9300-a-year for a senior day pupil.
Also last year, the school 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 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 it and the current establishment reopened the following year.
A secondary department was opened in 1973 and 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 called in receivers
The number of pupils enrolling in independent schools in Scotland has fallen by 3% since 2007.
Numbers enrolling in primaries have dropped
The school said they were not commenting at this stage.