"This long-standing open case is harming South African football," said Fifa secretary general Jerome Valcke in a statement published following a meeting with Sports Minister Fikile Mbalula.
"It is vital that this matter, which dates back to 2010, is concluded soon, with the culprits to be sanctioned in accordance with the zero tolerance policy."
Fifa found the results of pre-World Cup warm-up matches against Thailand, Bulgaria, Colombia and Guatemala in the weeks leading up the 2010 finals were fixed.
This briefly led to the suspension of South Africa Football Association (Safa) president Kirsten Nematandani who was later reinstated and was also present at Friday's meeting.
Fifa said the mandate of the judicial committee "will be limited to matters related to the case of irregularities related to friendly matches of the Safa in the build-up to the 2010 Fifa World Cup".
Michael Garcia, head of the judiciary arm of Fifa's ethics committee, could also join the commission, subject to constitutional approval.
"It is critical that structures are set up in order to tackle similar cases should they happen in the future," added Valcke.
"I am very pleased by the commitment of the South African government and also Safa to make sure this matter is now dealt with as a highest priority.
"Fifa will provide any advice and support possible both at investigatory and disciplinary level. To this effect a representative from Fifa's security division was also at today's meeting."
Allegations of match-fixing were first revealed in the press in July 2011 but Safa did not immediately act.
The issue was only raised once Fifa had incorporated the country into a wider investigation into Wilson Raj Perumal, a Singaporean jailed for two years for masterminding a match-fixing scheme in Finland.
Nematandani and four other top officials were briefly suspended following the handing over in December by Fifa to Safa of a 500-page investigation into the activities of Perumal and his Football 4U organisation.
But within a month their suspension was lifted on procedural grounds. – Reuters