The World Cup-winning former France international called on FIFA, UEFA and the English FA to take a strong lead after a spate of incidents brought the issue back into sharp focus.
"If you really want to fight racism, if you really want to show to the world that football wants to fight against it, you will have to use a deduction of points against clubs or kick them out of European competition," said Vieira.
"That will stop it, of course. If you kick a club out of Europe because they couldn't control their fans, it will happen once and I can guarantee it's not going to happen twice.
"If nothing is done, the situation will get worse and worse and you never know where things will go. Before we get to a place where you can't control it any more, you have to stop it straight away and the only way you can stop it is to have clear, strong punishments."
Vieira, who is Manchester City's football development executive, said English football was at a crossroads after high-profile race rows involving Chelsea's John Terry and Liverpool's Luis Suarez.
West Ham United's fans were also accused of racist chanting in their Premier League match against Tottenham Hotspur last week.
"I believe that Italy does not want to fight racism, for me that is clear," said the 36-year-old who played for Serie A's AC Milan, Juventus and Inter Milan.
"I hope that England is not going to be like that. I don't want England to get where Italy is because Italy will never fight against it, so as a black player, if you go to Italy you have to expect that and you have to accept it."
