The allegation was made by the estranged husband of Fabregas's partner Daniella Semaan at a High Court hearing in London.
A lawyer representing Elie Taktouk said police were investigating the sale of a property in London, where Mr Taktouk used to live with Ms Semaan.
But Mr Justice Coleridge said Mr Taktouk had a history of "lacking credibility", said he had heard evidence from estate agents about the property and added: "It seems to me as if it is a long shot."
The judge was analysing the latest stage of a dispute over money between Mr Taktouk and Ms Semaan at a hearing in the Family Division of the High Court.
Mr Taktouk had been ordered to pay Ms Semaan a £1.4 million lump sum following the break-down of their marriage, said the judge.
Ms Semaan is complaining that she is still owed nearly £1 million.
The dispute is due to be fully aired at a hearing later this year.
Mr Taktouk could be jailed if the judge rules against him.
"As a result of concerns expressed to the police, they are conducting a police investigation into the circumstances of the former matrimonial home being sold to Mr Fabregas's company," Martin Ward, for Mr Taktouk, told Mr Justice Coleridge.
"I am told by Mr Taktouk the police now have in their possession documentary evidence that a fraud had been perpetrated."
He said Mr Taktouk was alleging that the property had been sold at a "significant undervalue".
The judge told Mr Ward that he had heard evidence from "leading London estate agents" about the property at an earlier stage of the litigation and said: "Unless they are going to be implicated in the fraud it seems to me as if it is a long shot."
He added: "You client has ... a history of lacking credibility."
Mr Justice Coleridge said Ms Semaan had a formed a "permanent relationship" with Fabregas - a Barcelona, Spain and former Arsenal midfielder.
Mr Taktouk and Mr Semaan were at the hearing but not Fabregas.
Ms Semaan's lawyers said after the hearing that she did not wish to comment.