Visa’s chief executive says FIFA cannot deliver any meaningful reforms until Sepp Blatter has left his position.
Mr Blatter has insisted he will remain president of world football’s governing body until his successor is elected in February next year.
In June, he said he was resigning after the FBI charged 14 people with racketeering in a global investigation, including 10 football officials.
But Visa chief executive Charlie Scharf said FIFA’s response to the corruption crisis had been “wholly inadequate”.
He joined fellow sponsors Coca-Cola in demanding a fully independent reform commission.
Mr Scharf said: “We view the stewardship of our company, our brand and our clients with the utmost importance and try to hold ourselves to the highest standards.
“We seek to partner with those who think and act like us. I don’t believe that FIFA is living up to these standards.
“Furthermore, their subsequent responses are wholly inadequate and continue to show its lack of awareness of the seriousness of the changes which are needed.
“To this end, we believe two things need to happen to ensure credible reform. First, an independent, third-party commission led by one or more impartial leaders is critical to formulate reforms.
“Second, we believe no meaningful reform can be made under FIFA’s existing leadership.
“Football itself is a great sport with which we are proud to be associated.
“We want to be proud to be associated with FIFA and hope and look forward to working with them to that end.”
FIFA says it will meet its leading commercial partners next month following their demands for change.
“Clearly, there were a number of sponsors, mainly three, its Coca-Cola, McDonald’s and Visa, who have expressed and sent a letter to FIFA, asking for information,” FIFA Secretary General Jerome Valcke told a news conference in the Russian city of St Petersburg.
“Two or three days ago we received a letter from all of them offering to meet together, so there will be a meeting next month.”
Seven FIFA officials, including the then-FIFA vice-president Jeffrey Webb, were arrested in Zurich in May as Swiss police launched a separate criminal investigation into the award of the 2018 and 2022 World Cup tournaments.
Mr Blatter announced his departure in an attempt to ease the crisis.
He also announced his intention to introduce governance reforms at the same extraordinary congress that will elect his successor.
The announcement from Mr Scharf comes alongside the release of Visa’s third quarter earnings which showed the company beat analyst expectations by posting a 25% rise in net income to $1.7bn (£1.1bn).
The results sent Visa shares 7% higher in after-hours trading and are widely expected to reach an all-time intra-day high in New York trading.