Justice Teori Zavascki "denied the petition to issue a stay suspending the process," a court spokesman told AFP.
The decision all but erases the leftist leader's hopes of avoiding a six-month suspension and trial for manipulating the government's accounts.
It came down as the Senate held a marathon debate on impeachment, which was expected to end with a vote to suspend Rousseff for up to 180 days and put her on trial.
In court papers filed by the attorney general, Brazil's first woman president argued Cunha had used impeachment as a political weapon to wield against his opponents.
But the judge ruled the government's case lacked "legal plausibility.
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