However, Cricket Australia chief executive James Sutherland says head coach Darren Lehmann was not involved in the controversy and will remain in his post.
Sutherland added that the sanctions to be handed down to Smith, Warner and Bancroft within the next 24 hours will be “significant”.
He said: “It is not in the spirit of the game. It is not a good day for Australian cricket.”
Wicketkeeper Tim Paine has been named as captain for the rest of the series.
Matthew Renshaw, Glenn Maxwell and Joe Burns have been called up as replacements and will fly out to South Africa for the fourth Test, which begins in Johannesburg on Friday.
Sutherland told a news conference: “I share the anger and disappointment of Australian fans and the broader Australian community about events that unfolded in Cape Town on Saturday.
“On behalf of Cricket Australia, I want to apologise to all Australians that these events have taken place, especially to all kids who love cricket and idolise the players.
“I want to also apologise to Cricket South Africa and South African fans that this issue has overshadowed what should have been a great series.
“We recognise this issue goes beyond the technical nature of offences and various codes of conduct. It is about whether Australians can feel proud of their national sport teams.
“While the investigation is not complete, preliminary findings have been discussed by Cricket Australia’s board.” (Courtesy BBC)