Gary Lineker says it is "nauseating" to be involved in football after seven Fifa officials were arrested on charges of receiving more than £100m in bribes.
Swiss police made dawn raids in Zurich where officials were staying before Friday's presidential election.
A separate criminal investigation into how the 2018 and 2022 World Cups were allocated has also begun.
"It looks awful on the world governance of football, it is a wonderful sport," said the former England captain.
Match of the Day presenter Lineker, 54, has also called for a suspension to Friday's vote and for the bidding process for the World Cup in 2018, due to be held in Russia, and Qatar 2022 to be run again.
Fifa has already ruled out a revote, insisting the hosts would not change and "welcomed" the investigations, which it said it had instigated.
Fifa president Sepp Blatter, who is not among those arrested, has been in power since 1998 and faces Prince Ali bin al-Hussein of Jordan in Friday's election as he seeks a fifth term.
Gary Lineker's reaction in full:
How do you react to today's news?
I suppose it is surprising in terms of the timing and scale of it but I don't think any of us are particularly surprised about the allegations of corruption within Fifa.
There has already been many examples of that in previous years but I think it just shows you how deeply engrained within the corporation it is.
Fifa says it welcomes any investigations into wrongdoing, is it doing enough?
Fifa's clearly not doing enough. It's not done enough in terms of corruption that's for sure. Of course it says it welcomes investigations but how many people left in Fifa have not been accused of various wrongdoings.
It is quite clear that either Fifa needs to be completely transparent, they need to pretty much start again or it needs to be taken out of their hands. The major federations need to boycott Fifa.
If you got the English, the Germans, the Spanish, the Italians, the Americans, the Brazilians and major forces in world football come together and say we've had enough of this, it is time we come together and say listen we've had enough of this, it's time we do things differently more transparently, the way the game deserves.
Is there a will out there for this to happen?
I think this will help towards getting the result we'd all like and have wanted for some time. It will be interesting because Fifa tends to find a way of wriggling out of things.
In any other corporation, if there was so many things that were found to be corrupt, then the man at the top would go - but that doesn't seem to be the case with Fifa.
Sepp Blatter faces an election in two days' time, where does it leave him?
It wouldn't surprise me if the election went ahead and he walked away with it as he always seems to do. He has all the people he needs on his side, that's how you get money into your particular area of the world.
None of them would want to vote for someone that might lose because it weakens their position in Fifa. The election should be suspended for now - common sense should prevail - but common sense doesn't always exist in the towers of Fifa.
Should the 2018 and 2022 tournament bids be looked at again?
There are now major investigations not just concerning Fifa and corruption but also the two bids - World Cups 2018 and 2022 - so a lot will depend on how rotten it was and how corrupt the voting process was.
If it is substantial enough then I don't think they will have any option but to rethink and revote. It is a mess, it is a huge mess, but it is something that needs to happen and the sooner the better.
How does it look on the world governance of football?
It looks awful on the world governance of football, it is a wonderful sport. It is completely nauseating to be involved in football and have to suffer this ongoing embarrassment to the game that is the governing body.