The judge blocked the request because of concerns over Mr Assange's mental health and risk of suicide in the US.
Mr Assange, who is wanted over the publication of thousands of classified documents in 2010 and 2011, says the case is politically motivated.
Expressing disappointment at the ruling, the US justice department noted that its legal arguments had prevailed.
Its position is that the leaks broke the law and endangered lives.
"While we are extremely disappointed in the court's ultimate decision, we are gratified that the United States prevailed on every point of law raised," the justice department said.
The US authorities have 14 days in which to lodge an appeal and are expected to do so.
Mr Assange will now be taken back to Belmarsh Prison - where he is being held - and a full application for his bail will be made on Wednesday.
His lawyer Ed Fitzgerald QC told the court there would be evidence to show Mr Assange would not abscond.