The "damaging events" of the past week convinced Football Association vice-chairman David Gill to reject a place on Fifa's executive committee while Sepp Blatter is president.
Gill did not attend Saturday's first executive committee meeting following Blatter's re-election to a fifth term.
"My professional reputation is critical to me," said Gill in a statement.
Prince William, who is president of the Football Association, praised Gill's decision.
Speaking before Saturday's FA Cup final at Wembley, the Prince said: "I know I join with all of you in commending David Gill for his decision to stand down from the ExCo, and to lead by example by doing so."
He also described this week's events as Fifa's "Salt Lake City moment", referring to the incident in 1998 when the International Olympic Committee (IOC) faced similar allegations.
The Prince said: "Fifa, like the IOC, must now show that it can represent the interests of fair play and put the sport first."
Gill, who was due to sit on the committee as Britain's Fifa vice-president, had told the BBC before Friday's election that he would not take up his position should 79-year-old Blatter be re-elected.
The former Manchester United chief executive's statement added: "I simply do not see how there will be change for the good of world football while Mr Blatter remains in post.
"This action is not something I take lightly but the terribly damaging events of the last three days have convinced me it is not appropriate to be a member of the Fifa executive committee under the current leadership.
"I do recognise that Mr Blatter has been democratically elected and wish Fifa every success in tackling the many troubling issues it faces.
"I will continue to focus on my positions within the FA and Uefa, which I take seriously and am privileged to hold."
Blatter told a news conference: "He has given no excuse or reasons for his absence. Yesterday [Friday], he was installed officially as a member of the Fifa exco and I am waiting.
"When you are elected you do not come even to the first meeting. This is not responsible, if you are elected you have to come."
Gill, 57, was only elected two months ago for a four-year term. The British vice-presidency is elected by members of Uefa, European football's governing body, and an election for his successor is now likely to take place.
Blatter beat Prince Ali bin al-Hussein of Jordan in Friday's Fifa presidential vote despite a crisis which has seen seven Fifa officials arrested and a separate Swiss criminal investigation into the bidding for the 2018 and 2022 World Cups.