The friendly game had been scheduled to take place in Nyon, home to European governing body UEFA and its president Michel Platini.
"In a joint decision it was agreed to postpone the UEFA-FIFA challenge 2015, which had been scheduled for Friday, 2 October, until further notice," a FIFA spokesperson said on Wednesday.
On Tuesday, Swiss authorities said they were treating Platini as somewhere "between a witness and an accused person" in a probe that was widened last week to include FIFA President Sepp Blatter.
Attorney General Michael Lauber told reporters he did not rule out searching the Nyon headquarters of UEFA as part of the investigation.
Lauber's office has said Blatter is suspected of making a "disloyal payment" of 2 million Swiss francs (£1.3 million) to Platini in 2011 at the expense of FIFA.
Both men have denied any wrongdoing and said the payment was legitimate compensation for work Platini undertook for FIFA.
(Reporting by Simon Evans; editing by Andrew Roche)
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