There have been calls for Smith to step down or be sacked over the premeditated plan hatched during the lunch break on Saturday's third day in Newlands, after the captain admitted being the mastermind.
Australia Prime Minister Malcolm Turnbull weighed in on the incident Sunday, saying it "beggars belief" that role models such as Australian cricketers were "engaged in cheating like this".
Chief executive James Sutherland said Cricket Australia were "extremely disappointed and shocked" but added that the governing body wanted to get a clearer picture of the facts before making any decisions.
"I understand that that is not necessarily the fullness of response that everyone is looking for right now. But you will appreciate that there's an element of process that needs to be undertaken here," Sutherland told reporters in Melbourne.
"We will work very hard over the next couple of days to get to the bottom of it -- to understand the big picture, to understand the detail and to be making further comment on that in due course."
CA's head of integrity Iain Roy and head of team performance Pat Howard were flying to South Africa to conduct the investigation.
Television footage showed Smith's teammate Cameron Bancroft, 25, taking a yellow object out of his pocket while fielding in the post-lunch session and appearing to rub it on the ball.
He was later charged with attempting to change the condition of the ball.
Sutherland said he had not spoken to Smith but stressed repeatedly he was unhappy about the incident.
"I have very strong and clear views about the responsibility of the Australian cricketteam to play the game in the right spirit," he added.
"And I don't think anyone will be under any illusions as to what I think about this."
Smith, 28, has said he would not quit, adding: "I still think I'm the right person for the job."
The CA chief said Australian cricket fans had "every reason to wake up and not be proud of the team".
"This is a very sad day for Australian cricket. I'm not happy about this at all ... And I feel like Australian cricket fans feel right now."
There was widespread disbelief in Australia as the news hit the headlines on Sunday morning, with the significance of the incident evident when Turnbull added his voice to the chorus of displeasure.
Turnbull told reporters he had spoken to CA chairman David Peever, who reassured him that the body "will be responding decisively, as they should".
"The whole nation, who holds 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," he said.
"It's wrong and I look forward to Cricket Australia taking decisive action soon."
Government agency the Australian Sports Commission called for Smith and others involved or aware of the plan "to be stood down immediately" by CA as it completes the investigation.
Smith's predecessor Michael Clarke said he was feeling "pretty emotional" after the revelations.
"I can't believe if the leadership group has made a decision to do this, that they have gone and got the young kid (Bancroft) who is playing his eighth test match to do that," Clarke told broadcaster Channel Nine.
Clarke said he felt sorry for Smith, but added that the tampering was "blatant cheating" and "disgraceful".
Players' body the Australian Cricketers Association said it supported the investigation.
"It seems serious errors of judgement have been committed ... Cricket is a sport synonymous with the highest standards of behaviour," the ACA said in a statement.