"The players involved have officially been reported for breaching Cricket Australia's code of conduct," he added.
"I want to stress we are contemplating significant sanctions. These will reflect the gravity of the offences and the damage done to Australian cricket.
"We want to re-engage with Australian cricket fans and public to restore respect and pride."
Mr Sutherland said coach Darren Lehmann would not resign, contrary to media reports.
"He will continue to coach the Australian men's team under his current contract," Mr Sutherland said.
Cricket Australia has officially reported Smith, Warner and Bancroft for breaching article 2.3.5 of the Code of Conduct and the sanctions would be revealed in the next 24 hours.
Cricket community responds
Former Australian captain Michael Clarke says the Test team won't recover until everything about the ball-tampering scandal is revealed.
"To(o) many reputations on the line for the full story not to come out. Cape Town change room is a very small place!," he tweeted shortly after Cricket Australia boss James Sutherland announced only three players knew of the plan.
Former England captain Michael Vaughan told the BBC this incident has tarnished the values of the baggy green.
"This Australian team have got a huge identity problem. They’ve got a problem in the way that they are, they’re very self-righteous, they have been for a while," he said.
"To think that the leader Steve Smith has thrown out a young player to create sandpaper. Let’s get to the point. They’ve tried to create sandpaper out in the middle.
"That Australian baggy green cap that the players swear by… the actual values of that baggy green that we’ve heard for many, many years. This set of Australian players have completely ripped up those values."
Other members of the cricket community were not satisfied with Cricket Australia's response.
Details of their punishment are expected within the next 24 hours.
"These sanctions will reflect ... the damage it has done to the standing of Australian cricket."
A reporter repeatedly pushed Mr Sutherland on whether the trio "cheated", but Mr Sutherland refused to answer the question directly.
"This is not in the laws of the game, it's not in the spirit of the game, and again," Mr Sutherland said.
"It is not a good day for Australian cricket," he added.
Tim Paine has been officially appointed captain.
Matthew Renshaw, Joe Burns and Glenn Maxwell are on their way to South Africa to play in the fourth Test that starts on Friday.