Ged Stokes, who had travelled to South Africa to watch the cricket, was admitted to hospital on Monday with what was described as a serious illness. Ben Stokes missed practice on Tuesday to be at his father's bedside.
The statement said the Stokes family thanked people for their support of the family and in particular the medical practitioners who had treated Ged Stokes.
Although fast bowlers Stuart Broad and Jofra Archer appeared to have recovered from illness, which caused them to miss England's two warm-up matches, three players - Jack Leach, Ollie Pope and Chris Woakes - missed the team's final practice because of illness.
The statement said the three ill players had not been ruled out of selection for the Test.