According to prosecutors, the money was obtained illegally and not declared.
Eduardo Cunha denies the charges and says he is being unfairly targeted by the Prosecutor’s Office.
He has been leading calls for the impeachment of President Dilma Rousseff, but he is now facing calls from other parties to step down.
As speaker of the Chamber of Deputies, Eduardo Cunha holds the power to allow impeachment proceedings against Dilma Rousseff.
The main opposition parties made public a demand last week for Eduardo Cunha to resign.
A request for his resignation had already come from government supporters in Congress.
Eduardo Cunha is being investigated for alleged corruption in a kick-back scheme at the state run oil company, Petrobras.
Brazil’s Supreme Court ruled on October 15 that the Prosecutor’s Office was allowed to investigate allegations of corruption against Eduardo Cunha.
Prosecutors said on October 16 that Eduardo Cunha hid millions of dollars in Swiss accounts opened in his wife’s and his children’s names.
“There is sufficient proof that the foreign bank accounts were not declared and that at least in relation to Eduardo Cunha the money was obtained illegally,” said a Prosecutor’s Office statement.
A Brazilian audit court ruled earlier this month that President Dilma Rousseff broke the law in managing last year’s budget.
Dilma Rousseff was accused of borrowing money illegally from state banks to make up for budget shortfalls.
Government supporters say calls for an impeachment less than a year after Dilma Rousseff was re-elected are tantamount to a coup attempt.
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