The second-in-line to Britain's throne is a fan of what is referred to as the "beautiful" game and is also the President of the UK's Football Association (FA).
"There seems to be a huge disconnect between the sense of fair play that guides those playing and supporting the game, and the allegations of corruption that have long lingered around the management of the sport internationally," the royal said during a speech at Wembley Stadium in London.
"Those backing FIFA, such as sponsors and the regional confederations, must do their bit to press these reforms - we are doing football and its fans no favours if we do not. I have no doubt that when FIFA reforms, its mission to spread the benefits of the game to more people, especially those in developing countries, can only be enhanced," the 32-year-old prince said.
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The seven, arrested in Zurich earlier this week, are among 14 indicted on charges of bribery, racketeering and money-laundering, involving tens of millions of dollars since 1991.
Meanwhile, Swiss authorities have launched a separate criminal investigation into the awarding of the 2018 and 2022 World Cup tournaments to Russia and Qatar.
The prince led England's bid team for the 2018 finals, which also included Prime Minister David Cameron and football star David Beckham among others.
The Duke of Cambridge also said that the FA, the sport's governing body in England, had been taking a critical look at itself under Greg Dyke's leadership and could become the "gold standard of sporting governance".
"I feel we need to ensure that we become the gold standard of sporting governance. A modern, transparent and inclusive organisation - representative of the broad and diverse society who play and love our game.
"Over the next few years, if we want credibility to influence the debate on reform in FIFA, we must continue to strive for excellence in our own organisation.
Blatter is not named in the indictment and denies having anything to do with an alleged USD 10-million-bribe.