Goalkeeper Galekovic joins Socceroos
"It has been decided that Jones will not be returning to South Africa and will remain with his family," the team said in a statement.
Jones, a regular understudy to first choice Mark Schwarzer, left almost a week ago before the start of the finals which kicked off with South Africa playing Mexico on Friday.
FIFA granted Australia's football federation special permission to replace the player with fellow back-up keeper Galekovic ahead of the Socceroos' opening Group D match against Germany on Sunday.
Galekovic was already in South Africa and had been practising with the squad despite not officially being part of the team.