The judge blocked the request because of concerns over Mr Assange's mental health and risk of suicide in the US.
The 49-year-old is wanted over the publication of thousands of classified documents in 2010 and 2011.
The US claims the leaks broke the law and endangered lives. Mr Assange has fought the extradition and says the case is politically motivated.
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 will be evidence to show Mr Assange will not abscond.
District Judge Vanessa Baraitser ruled that while US prosecutors met the tests for Mr Assange to be extradited for trial, the US was incapable of preventing him from attempting to take his own life.
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