Christ Church Early Learning, on Quay Road, has had to close because of money struggles.
A spokesman for the directors/trustees of Christ Church Community Services - which runs the pre-school - said the coronavirus lockdown had compounded existing financial difficulties.
“We would need to find £50,000 to tide Christ Church Early Learning over the next few months, and even then there would be questions on the viability of the setting,” he said.
“The staff over the last two years have performed valiantly to turn the preschool into an OFSTED Good rating – but the finances kept undermining their good work.
“We would like nothing better than to see funding come into place to save a setting like ours.
"There seems very little capacity for our local education authority to help because central government has underfunded early years for a very long time.”
Among those shocked at now having to find another nursery for their child is Kirsty Fletcher, of Flamborough.
Her daughter Portia’s condition - which causes her skin to blister and tear at the slightest touch - means she needs specialist care.
Kirsty is concerned she will not be able to get elsewhere.
She rang around 19 nurseries trying to find a place for Portia and Christ Church Early Learning was the only one willing to take her.
The five-year-old has deferred starting primary school because her family and experts have agreed she is not ready.
“This will have a massive impact on her,” said Kirsty.
“Portia isn’t physically or mentally ready for mainstream school.
“Her needs are complex and staff need to be medically trained and able to meet her needs."
The nearest school that may be able to accommodate Portia is Kings Mill in Hull but Kirsty says her daughter is not yet ready to go there and with twin older brothers at school in Flamborough, she would struggle to get all her children to school on time.
“Portia wouldn't be the girl she is today without the nursery.
"She has come on leaps and bounds since starting there,” she added.