Mr McAleavey said the scale of the job losses was unprecedented.
He is seeking an emergency meeting with Northern Ireland's first minister and deputy first minister to address the issue.
Groups in the environment, the arts and training are affected by the cuts.
"Skilled staff will be lost from our sector and the impact will be felt right across Northern Ireland with a loss of local walking routes, arts events and childcare facilities," Mr McAleavey said.
"Voluntary and community organisations provide highly specialised services in areas where government provision doesn't meet the needs of local people and often work with harder to reach client groups.
"It is obvious that the most vulnerable people will be harder hit with programmes focusing on training and support to help people get jobs, develop crucial early learning skills in children and rehabilitation being cut."
Among the worst hit is the Early Years organisation which promotes childcare.
It has lost a £2m grant from the Department of Education and said more than 170 jobs are under threat.
NICVA has been collecting data on how it believes the cuts will hit various organisations and assessing the impact on their funding streams, jobs and members of the community.
Siobhán Fitzpatrick, chief executive of Early Years, said it was a "worrying time for parents and staff in early years settings".
"We fully appreciate the difficult economic decisions that have to be made but early years is not the right area to target," she said.
"The impact of this on 153 communities, 2,500 children and 177 jobs across Northern Ireland will be devastating in the short and long term."
Marie Cavanagh of Gingerbread, which provides free advice, training, and practical support for single parents, said it lost five of its staff this week through redundancy, with another position also expected to go.
She said it represented a third of their workforce, and as well as the human cost in terms of jobs, it meant "lone parents are the losers".
Ms Cavanagh said the organisation had supported more than 1,300 lone parents to train and undertake essential workplace activities, over the past 25 years.
She said Gingerbread had applied for around £195,000 from the European Social Fund for 2015/2016 as part of a three-year application, but had received nothing.
It had been running a programme, Marks & Start, which combined three days of pre-employment training with a two-week work experience placement with Marks & Spencer.
Gingerbread had hoped to widen the scope of the programme this year.
"Over 50% of those who did the Marks & Start programme got some form of employability, we hoped to widen it out to 300 lone parents," she added.
"Three hundred lone parents have lost the opportunity to train and experience employment which would have benefited their families and children and could have led to employment."
Karen Sweeney, director of the Women's Support Network, said the cuts would have "long-lasting effects in terms of supporting vulnerable families, those with mental health issues, tackling unemployment, reducing child poverty and the provision of accessible childcare".
Ulster Unionist assembly member Robin Swann said: "I am concerned that cuts in funding for training in the community sector will affect the most vulnerable in our society who have no other avenues to fund their support programmes."
Mr Swann, who is chairman of Stormont's Employment and Learning Committee, said the issue was "particularly acute since the minister ceased funding the Community Family Support Programme, and the Collaboration and Innovation Fund".
"The minister has presided over this shambles, but the parties who voted through the 2015/16 budget also need to answer the questions coming from the community as to why their programmes have been scrapped so abruptly," he said.
Northern Ireland Council for Voluntary Action (NICVA) chief executive Seamus McAleavey has warned hundreds of job losses are likely as a result of cuts in the sector.