South Africa batsman Jacques Kallis was ruled out of this week's first Test against England on Monday.
South Africa media manager Gerald de Kock said: "He is not in our plans for the first Test at least.
"There was a possibility that he would be on a flight today but that's now not going to happen."
The first of five Tests starts on Thursday at Edgbaston.
"It might be a week, it might be a month. He's being given as much time as he needs," de Kock added.
The 27-year-old Kallis is South Africa's in-form batsman, as well as a genuine all-rounder.
He hit back-to-back centuries during a just-concluded one-day triangular series against England and Zimbabwe, averaging 109.66 during the tournament.
Kallis averages more than 50 in Tests and has also taken 174 wickets at 30.43 each.