The FSCS compensates the first £50,000 of investments lost if a financial services firm is unlikely to be able to pay what is due.
But unincorporated associations, including charitable trusts, have until now been excluded from claiming compensation if they have assets of more than £1.4m.
The FCA, one of two financial services regulators that replaced the Financial Services Authority earlier this year, said those trusts will be able to claim on the FSCS if they do not exceed two of the three criteria: a turnover of £6.5m, a balance sheet total of £3.26m, and 50 employees.
Unincorporated associations that were not able to claim during the collapse of Icelandic banks in 2008 may now be entitled to compensation.
The FCA said it was "not aware that any claims were wrongly rejected", but would "consider claims from claimants who believe they may be eligible for help".
The FCA estimates these changes would apply to 5,000 associations and 24,000 partnerships, many of which will be charities.
The changes affect only investments, not deposits.
The FSCS also provides £85,000 cover for depositors who lose their money. The Prudential Regulation Authority, the other regulator replacing the FSA, is consulting on proposals to clarify the compensation rules for deposits so that in the future all unincorporated associations, regardless of size, are within the scope of FSCS cover for deposits.
Jane Tully, head of policy at the Charity Finance Group, said that she was pleased by the decision, but that it would affect relatively few organisations.
"Most large charities are incorporated anyway," she said. "But this is a positive step. We have argued that charities, given their public benefit status, should be liable for FSCS protection regardless of size."