The ex-Manchester United defender and England coach said the threat of a World Cup boycott from the game’s biggest names would bring the governing body “to a standstill”.
Writing in his Daily Telegraph column, Neville said he normally believed players should “stay out of the politics of the game”.
He wrote: “However this is about players wielding their power against corruption. I would expect management committee members of PFA’ s around the world to demand to know what could be done to ensure that the voice of the players was heard.”
Neville, a Sky Sports pundit, said the world football players’ union, FIFPro, should be “canvassing the opinion of every national team captain in the world to find out their views and feelings about the situation”.
“I am not suggesting that players should go out on a limb by going on strike, but Fifa and Blatter would be nothing without the players,” he wrote. “It would need to be a co-ordinated and united force.
“Just think of Cristiano Ronaldo and Lionel Messi, the two biggest stars in the game right now, and consider a World Cup without those two.
“The tournament would not exist if Ronaldo and Messi turned their backs on the World Cup because of the way Fifa is running the game. This would impact sponsors and broadcasters and in turn bring this whole debacle of an organisation to a standstill.”
Neville’s comments came after under-fire Sepp Blatter was voted in for four more years as Fifa president, despite the arrest of seven Fifa officials on corruption charges.
More than a third of FIFA’s 209 associations voted for Prince Ali Bin Al Hussein of Jordan as significant numbers turned against Mr Blatter following the crisis that has struck the world governing body this week.
The Swiss bureaucrat, 79, won the first round by 133 votes to 73, but he failed to gain a two-thirds majority, and Prince Ali, the 39-year-old Sandhurst graduate, then withdrew from the contest rather than force a second round of voting.
The election in Zurich was held amid the continuing fall-out from the arrest of seven Fifa officials in the city and a total of 18 people connected to football indicted on corruption charges by the US justice department.
Football Association chairman Greg Dyke, who had earlier backed the idea of a co-ordinated European boycott of the World Cup, said: ‘’This is not over by any means. To quote the Attorney General this is the beginning of the process, not the end.”
Mr Blatter had told the 209 associations who gathered for the Fifa Congress that the crisis would not have happened if countries other than Russia and Qatar had won the vote for the 2018 and 2022 World Cups.
In what appeared a reference to the United States and England losing out, Mr Blatter called for unity.
Most of the media investigations into Fifa have come from Britain, while it is the US justice authorities whose actions led to the indictments of 18 people, including charges that a Fifa bank account was used to channel a 10million US dollar (£6.54million) World Cup voting bribe.
Mr Blatter said: “If two other countries had emerged from the envelope I think we may not have these problems.”