The senior men's national team, led by coach Hugo Broos, had been scheduled to leave OR Tambo International Airport on Sunday evening aboard a charter flight bound for Mexico City and then heading to their base camp in Pachuca, located just under two hours away.
However, the public broadcaster has been informed that at least 20 members of the travelling party, the majority of them players, still have their visas being processed at the United States Embassy in Johannesburg.
It is also understood that one or two members of the technical team have had visa applications declined, prompting SAFA to work urgently behind the scenes to resolve the matter.
The delay comes as Broos had hoped to maximise preparation time ahead of South Africa's first World Cup appearance since 2010. SAFA CEO Lydia Monyepao recently revealed to SABC Sport that the association had lined up a practice match against Jamaica on 5 June as part of the team's preparations.
Bafana Bafana have been drawn in Group A alongside hosts Mexico, Czechia and South Korea, with their opening fixture scheduled for 11 June at Estadio Azteca.
While it remains unclear where responsibility lies for the latest setback, it adds to a growing list of administrative challenges that have affected the national team in recent years.
The most recent was the blunder of Teboho Mokoena's suspension during the World Cup qualifiers and FIFA eventually docking Bafana three points from the victory over Lesotho in which the midfielder was ineligible to play.
At the time, fingers were pointed at team manger Vincent Tseka but Broos said everyone within the association was to blame. ¨¨Despite those obstacles, South Africa secured qualification after an impressive campaign, finishing top of their group ahead of Nigeria, Benin, Lesotho, Rwanda and Zimbabwe.