Cricket Australia CEO James Sutherland said: "In view of the broader reputational and integrity issues involved, the sanctions that will be contemplated are significant".
The players were reported for breaching article 2.3.5 of CA's code of conduct.
Earlier Cricket Australia announced that Smith, Warner and Bancroft were being sent home from Johannesburg and replaced by three other players for the fourth Test.
Young batsman Cameron Bancroft, caught on camera tampering the ball on the third day of the Cape Town Test against Australia has been banned for a period of nine months.
Smith has already been suspended for one Test and docked his entire match fee by the International Cricket Council (ICC) for his role in the affair.
"He's distraught. Very upset", Sutherland said of the fresh-faced skipper, renowned for being an emotional character on and off the field.
Sutherland said that Lehmann will continue in the capacity of coach with the team.
New Zealand take on England and in the video Smith is asked if he can help the Kiwi bowlers to get some swing, legally, adding help from Warner and Bancroft would also be welcome.More news: Toronto ultrasound technician charged with sexual assault
About Smith and Warner's participation in the upcoming edition of the Indian Premier League, Sutherland said the participation will depend on the sanctions and what the Indian cricket board, BCCI makes of it. For someone like Warner, setting him aside from Smith and Bancroft, he is a person who does need to really have a good look at himself and the way he goes about playing cricket.
'I want to apologise to all Australians.
"Australia's core values of respect, integrity and fairness must be brought to bear on the game of cricket through such a process", it said.
A report in ABC news confirmed the development.
Australian cricket captain Steve Smith departs from Cape Town International airport.
He has been stripped of the Australian captaincy, which is being taken over by Tim Paine on a full-time basis. Bancroft was tasked to do the on-field tampering - roughing up one side of the ball - but botched it when he was caught by television cameras doing the tampering and then trying to hide the tape down the front of his pants.
Australia also lost the test by a crushing 322 runs.
He famously punched England's Joe Root in a bar before the 2013 Ashes while - in the current series in South Africa - he had to be restrained while arguing with Proteas wicketkeeper Quinton de Kock in a stairwell at Kingsmead and confronted a spectator in Cape Town before his involvement in the ball-tampering plot.
The bans leave the careers of the players on hold, but the damage to the reputation of all three will likely be much more long-lasting and for Warner, 31, it may well spell the end of his global career.