Businessman Chagaev, 51, is under investigation after media reports suggested he had submitted a falsified document to prove his solvency during a bankruptcy trial.
"Prosecutor Yves Bertossa confirmed a charge of written forgery without commenting further," a spokesman for the public prosecutors office was quoted by the Sports information agency as saying.
The football boss was questioned during a lengthy session on Thursday before leaving with lawyer Jacques Barillon, who told waiting journalists his client had been asked about his dealings and also "other people and associations" linked to the affair.
A prosecutor in the canton of Neuchatel said last week that a Bank of America document provided by Chagaev stating that he held $35 million was not produced by the institution.
Barillon said Chagaev told the hearing he had not written the document in question but he recognised that it did not come from the Bank of America.
The businessman, also facing allegations of attempted fraud, could face five years in jail if found guilty.
Over the past fortnight, the Swiss courts have searched the Geneva offices of two of Chagaev's companies, his home in Saint-Sulpice near Lausanne and the office of Neuchatel Xamax.
Chagaev's ownership of Xamax has been controversial in Switzerland -- earlier this season he sacked the entire coaching staff after the side lost 2-0 to Basel.
More recently, the Swiss Football League fined the club 20,000 francs (€16,440) for flouting licensing rules, after they failed to respond to queries over their budget.