The 35-year-old has failed to recover from a shoulder injury suffered during the year's Indian Premier League. South Africa hope to have him back in time to face Bangladesh in their second match on Sunday.
"Dale is not quite ready yet," said Gibson. "He is not far away but he is not ready yet. We think with a six-week tournament there is no real need to force the issue so he won't be available.
"We know he is close and is getting closer every day. We will give him as much time as he needs to get ready. I am trying to give a date but we are hoping if not Sunday, then certainly by India (next Wednesday)."