Umbrella body the Northern Ireland Council for Voluntary Action, has requested an urgent meeting with Secretary of State Paul Murphy to discuss the cuts, which it claims could reach £30m.
Nicva says that efficiency savings designed to enhance frontline services are in fact having the opposite effect.
"The reductions are the perverse result of financial planning by government departments which is turning public policy on its head," said Nicva chief executive Seamus McAleavey. "The idea is to cut bureaucracy and divert resources to front-line services. In practice, it is services to the public, and especially to disadvantaged groups and individuals, that are suffering."
Nicva is warning that at least two major voluntary sector service programmes are to be wound up. The £5m Children's Fund, which supports children in need and young people at risk, is coming to an end. Worktrack, a £10m programme through which unemployed people not eligible for the New Deal are trained by voluntary and community groups, will also cease taking new trainees at the end of the year.
In addition, Nicva says one of Northern Ireland's 14 NHS trusts is cutting £1m from its grant budget to the voluntary sector. One voluntary organisation working in preventative health is to suffer a grant cut of £65,000.
"There are also worrying signs of big reductions in other services," said McAleavey. "Education has received most attention, but the axe is also falling on services such as the arts and sport which are delivered successfully by voluntary bodies. In addition, the Children's Fund is being brought to an abrupt end despite government's commitment to eradicate child poverty."
However, a spokesman for the Department of Finance and Personnel in Northern Ireland said the situation was not as bad as feared.
"The draft Budget is currently the subject of a consultation exercise," he said. "However, proposals contained within it include substantial sums for a wide range of services and support for children and their families."
He added: "Spending from the Children's Fund, amounting to some £40m over six years, was one small element of this.
"Of that total, almost £15m is included in the draft Budget to provide to existing projects. Allocations previously made are therefore not being withdrawn."
But McAleavey called for "corrective action to preserve and protect important services delivered to the public by voluntary and community groups".