Smith said that the team's "leadership group" had a plan, carried out by batsman Cameron Bancroft, to tamper with the ball to "get an advantage".
Smith will now miss the fourth and final Test of the series, and he has also been sacked from his lucrative position as captain of the Indian Premier League's Rajasthan Royals side.
Australian government agency, the Australian Sports Commission, is calling for the Smith to be immediately removed.
It's also calling for any other members of the team leadership group or coaches who knew about the scheme to also go.
Vice-captain David Warner has been stood down from his position for the rest of the match.
Bancroft was fined 75 percent of his match fee and given three demerit points.
Smith admitted a charge of conduct "of a serious nature that is contrary to the spirit of the game", said a statement from the International Cricket Council, the sport's governing body.
"As captain, Steve Smith must take full responsibility for the actions of his players and it is appropriate that he be suspended," said ICC chief executive David Richardson.
Smith said he was embarrassed and took responsibility for the actions of his side but he would not be stepping down as skipper permanently.
To compound matters for the Australians, they saw all 10 wickets fall in the final session on day four to lose the match by 322 runs.
The final match of the ill-tempered series begins in Johannesburg on Friday.
Lawrence Booth, editor of Wisden - a cricket almanac - told Morning Report the real punishment will come from Cricket Australia who is currently investigating.
"I think we will see much tougher action from [Cricket Australia]. If you've got the prime minister calling for Smith to go I don't think that the board is going to stand in the way of that.
"I think they will reflect the general sense of outrage in Australia."
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 four-match series, which is level at 1-1.
Television footage showed Bancroft take what he said was yellow tape out of his trouser pocket before rubbing the ball.
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".
Cricket Australia (CA) has begun an investigation into the actions of its team, which Australia's prime minister Malcolm Turnbull said had "shocked and bitterly disappointed" him.
"The game needs to have a hard look at itself," added ICC chief Richardson.
"In addition, and most importantly, member countries need to show more accountability for their teams' conduct.
"Winning is important but not at the expense of the spirit of the game which is intrinsic and precious to the sport of cricket. We have to raise the bar across all areas."
Batsman Bancroft admitted changing the condition of the ball and accepted his punishment from Andy Pycroft, who is on the elite panel of ICC match referees,
"I acknowledge that Cameron has accepted responsibility for his actions by pleading guilty to the charge and apologising publicly.
"As a young player starting out in international cricket, I hope the lessons learned from this episode will strongly influence the way he plays the game during the rest of his career."
Players who accumulate four demerit points in a two-year period receive a one-match ban, while those who get eight demerit points in the same 24-month period are banned for two matches.
Neither Smith nor Bancroft had any demerit points on their records before the current incident.
Prior to the start of the fourth day's play in the third Test, CA chief executive James Sutherland said Smith and David Warner had "agreed to stand down as captain and vice-captain respectively for the remainder of this Test match".
Wicketkeeper Tim Paine was appointed acting captain for the rest of the match, although Smith and Warner continued to play.
"This Test match needs to proceed, and in the interim we will continue to investigate this matter with the urgency that it demands," Mr Sutherland said.
"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."
CA's head of integrity Iain Roy and head of team performance Pat Howard have also travelled to Australia.
Photo caption: Steve Smith, left, captain of Australia with team mate David Warner.