The former Arsenal captain believes only points deductions or exclusion from competition will be severe enough to force clubs to commit to tackling their racist fans.
Vieira, now Manchester City's football development executive, thinks the penalties should be much more severe than simply fines and insists points deductions or bans from competition should be enforced.
"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 competition," Vieira told the Times. "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 will guarantee it's not going to happen twice."
The Frenchman warns that a lack of serious action to tackle the problem will only allow it to grow.
"If nothing is done, the situation will get worse and worse and you never know where things will go," Vieira said. "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.
"Of course, we all need a second chance, we all need to realize that we are doing something wrong, but if you do it again the punishments should be really hard."