Smith said on Saturday that the team’s "leadership group" had spoken about a plan to tamper with the ball, carried out by batsman Cameron Bancroft.
Tim Paine will be captain for the rest of the match, although Smith and Warner will continue to play.
The match is into its fourth day.
"This Test match needs to proceed, and in the interim we will continue to investigate this matter with the urgency that it demands," said Cricket Australia chief James Sutherland.
"Cricket Australia and Australian cricket fans expect certain standards of conduct from cricketers representing our country, and on this occasion these standards have not been met.
"All Australians, like us, want answers and we will keep you updated on our findings, as a matter of priority,"
The ball-tampering incident took place on the third day of the third Test in Cape Town - escalating the tension around what has been an ill-tempered series.
Television footage showed Bancroft take what he said was yellow tape out of his trouser pocket before rubbing the ball.
The 25-year-old has been charged by the International Cricket Council (ICC) with attempting to change the condition of the ball - which is prohibited by Law 41.3.
Smith said after play that it was a "big mistake" but that he would not stand down. He said the team’s "leadership group" had spoken about the plan and "thought it was a way to get an advantage".
The Australian Sports Commission (ASC) called for Smith "to be stood down immediately, along with any other members of the team leadership group or coaching staff who had prior awareness of, or involvement in, the plan".
Prime Minister ’shocked and disappointed’
Australian Prime Minister Malcolm Turnbull has also spoken about the issue.
"I am shocked and bitterly disappointed by the news from South Africa," said Turnbull.
"It seems beyond belief the Australian cricket team have been involved in cheating. Our cricketers are role models and cricket is synonymous with fair play. How can our team be engaged in cheating like this? It beggars belief."
Turnbull later added: "I have spoken with David Peever, the chairman of Cricket Australia, and I have expressed to him very clearly and unequivocally my disappointment and concern. He has said to me that Cricket Australia will be responding decisively, as they should.
"It’s their responsibility to deal with it, but I have to say that the whole nation, who hold those who wear the baggy green up on a pedestal - about as high as you can get in Australia, certainly higher than any politician, that’s for sure - this is a shocking disappointment."
