Extern says it has been told the Intensive Family Support Service (IFSS) must close with the loss of 47 jobs.
It says the service supports 235 families affected by issues including poverty, mental health, and addiction.
The Health and Social Care Board said the scheme was operated "on a pilot basis" for three years from 2014.
Charlie Mack of Extern said he had support from parties across the political spectrum before the election.
"I have in writing from (DUP leader) Arlene Foster two days before the election saying she was personally supportive of the project".
Mr Mack described the decision as "devastating" and "a complete false economy".
He said: "IFSS is a life-altering, and often life-saving service, which is seeing 50% more children in Belfast being removed from the child protection register, is keeping children in school, and is significantly reducing anti-social and violent behaviours".
The Health and Social Care Board said it was "working with the Belfast Trust to ensure minimum disruption and impact to these families as the pilot comes to an end".
In a statement, the Department of Health said the pilot had come to an end and there were similar levels of need across Northern Ireland:
"Our focus now will be on taking the learning from the pilot in Belfast and applying it not only to statutory family and children's services but also to other family support services."
The department said families, "will continue to be supported by statutory services, where appropriate, or connected with other non-statutory family support services in the area".
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A Northern Ireland charity says children will be the first victims of the Stormont collapse as one of its projects is to close.