SAFA did not exonerate the group, which included president Kirsten Nematandani, new chief executive Dennis Mumble and its top refereeing officials, but said the committee that put them on "special leave" did not have the authority to do so.
The move comes less than two weeks before South Africa hosts the African Nations Cup finals.
Last month, world soccer governing body FIFA handed over a 500-page report to SAFA on its investigation of convicted Singapore match fixer Wilson Raj Perumal and his Football 4U organisation.
The FIFA report alleged the results of South Africa's pre-World Cup warm-up matches against Thailand, Bulgaria, Colombia and Guatemala leading up the 2010 finals were fixed and implicated the nation's officials.
"We are not sweeping this under the carpet," SAFA spokesman Dominic Chimhavi told reporters, adding the matter would be thoroughly investigated.
Allegations of match fixing were first revealed in the South African press last July but SAFA did not immediately act, only raising the issue once FIFA had incorporated the country in a wider investigation into Perumal.
The organisation's image has suffered in recent years from in-fighting between football politicians and near bankruptcy, with an independent audit firm brought in to run the body's finances.
SAFA was hoping a successful Nations Cup tournament, kicking off on Jan. 19, would help reverse its fortunes and recently unveiled a long-term development plan to revive corporate sponsorship. (Reporting by Jon Herskovitz; Editing by John O'Brien)