Had the judge ruled in Mr Assange's favour, he would have been free to leave the embassy without being arrested on the British warrant.
He has said he feared Sweden would hand him over to the United States to face prosecution over Wikileaks' publication of leaked USA military and diplomatic documents.
After the decision, Assange's lawyer Mark Summers asked her to consider whether it would be in the public interest to continue pursuing his client for breach of bail conditions. Last year, WikiLeaks released documents detailing USA government hacking tools. She said the Ecuadorean government is seeking a "dignified and just" solution in his case with the British government. "This is and has always been our overriding concern".
Ahead of Tuesday's ruling, a small group of Assange supporters gathered outside the court in central London.
It is not publicly known whether there is a sealed USA indictment against Assange.
Assange has been staying - virtually imprisoned, he says - at the Ecuadoran Embassy for five years.
Ecuador, which made Assange an Ecuadorian citizen last month, has urged the United Kingdom to grant him diplomatic status so that he may leave the embassy without fearing arrest. However, with the arrest warrant upheld, Assange can't step onto the streets of London without risking arrest.
That apprehension related to "what might happen to him in America as a result of extant legal procedures" as well as "what has happened to others", Mr Summers said.
However, Metropolitan Police in London said Mr Assange will still be arrested - for failing to surrender to a court - if he leaves the embassy.