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.