Model, actress and radio personality Pearl Thusi was in a car accident that left her and her daughte.
A Fifa spokesman confirmed to Times Media yesterday: "The match has to be played on neutral ground."
The decision comes amid reports of fresh fighting in CAR capital Bangui, where rebels recently killed 13 SA National Defence Force soldiers and overthrew former president Francois Bozize.
Fifa has decided that the security of the South African squad cannot be guaranteed and therefore a potentially difficult trip has now been avoided.
Bafana coach Gordon Igesund had been concerned that his players may have been intimidated by the surreal atmosphere of Bangui and the events that have taken place there in the past few months.
Igesund acknowledged that getting peak performance out of the squad under such circumstances would have been difficult and so this announcement will come as a major boost to his chances of getting the team to the World Cup next year.
The CAR federation must decide on a new venue, likely to be in Cameroon or Point Noire, Congo. That decision only has to be taken at the end of the month.
South Africa play two away matches in June, seeking to keep alive their hopes of going to Brazil. Avoiding a trip to Bangui gives new hope that Bafana Bafana might be able to pick up valuable away points in their battle to finish top of Group A and qualify for the last round of play-off matches.
There is a precedent for South Africa. Bafana had a lucky break in the 1998 World Cup qualifier when the overthrow of the Mobutu Sese Seko regime coincided with the scheduled qualifier against the then Zaire in Kinshasa. Fifa moved it to neutral Togo where Bafana won and went on to top the group and qualify for a first-ever finals appearance in France.