Parents at the independent Tavistock and Summerhill school in Haywards Heath received an email on Monday saying it would not reopen after half term.
A notice on the school gate said it had been placed into voluntary liquidation.
Governors said the closure was regrettable and that they were grateful to teachers, parents, suppliers and benefactors for their support.
Elaine Prentice, whose three-year-old daughter attended the nursery school, said the way parents had been treated was very sad.
"A lot of them are very upset. We have only got four days to find a new school," she said.
"The governors must have known in September that things were bad, but new staff were taken on."
A spokesman for West Sussex County Council said parents of children at the school who wished to apply for a place at local maintained schools should contact the pupil admissions team.
"We aim to process in year applications within 10 school days," he said.
RSM Restructuring Advisory Ltd said it had been instructed to assist the directors in preparing the school to be liquidated, but had not been appointed as liquidators.
The school has places for 100 pupils from reception to year eight and 50 pupils in the nursery.
The email said there had been a significant drop in pupil numbers during the summer months.
It added that a team had been appointed to develop a long-term funding strategy for the school, but it was unable to remain solvent to implement it.
Ms Prentice said she had paid Â£1,400 in advance for her child to attend the nursery two days a week this term, but would have to attempt to recover the money from the liquidator, RSM UK in Crawley.
The school board said there had been numerous attempts to secure the long-term future of the school over the past five years.
"During this year, a number of alternative management structures had been proposed, all of which have ultimately proved to be unviable," it said in a statement.
A creditors' meeting is to be held in November.
A West Sussex preparatory school has closed after failing to attract enough pupils to cover its overheads.