The Communities and Local Government department is setting up the £7.5m fund to help registered charities run community schemes.
But a consultation document on the proposals, to which interested parties can respond until the end of the month, proposes that charities with income less than £400,000 cannot apply.
A spokeswoman for umbrella body the NCVO, which is among the signatories, said organisations that could deliver the programme's objectives should not be squeezed out because of their size.
Other government departments have introduced similar income thresholds, prompting claims of discrimination against smaller charities.
The Department for Children, Schools and Families' Youth Sector Development Fund requires organisations to have an average annual turnover of at least £1m over a three-year period, and the Department of Health's Third Sector Investment Programme will only award grants that do not exceed 25 per cent of a charity's income.
"What really got the alarm bells ringing was the fact that the restrictions have appeared in funding programmes across several different departments," said Jay Kennedy, policy officer at the Directory of Social Change.
Arbitrary thresholds should be abandoned, said Kennedy. "The driving factor, surely, is the department's desire to cut down on administrative hassle," he said.
John O'Sullivan, chief executive of St Johns Housing Trust, a small homelessness charity in Suffolk, said: "If we continue on this path, they will shake out a good portion of the voluntary sector and diversity will be lost."
A Cabinet Office spokesman said small groups could benefit from grant programmes designed specifically for them, including the £130m Grassroots Grants fund.