Assange was due to be released on September 22 after serving his sentence for breaching bail conditions. But Westminster Magistrates' Court heard that there were "substantial grounds" for believing he would abscond again, according to the BBC.
The 48-year-old Australian is fighting extradition to the US over allegations of leaking government secrets. He will face a full extradition hearing in 2020, starting on February 25, after an extradition request was signed by the then Home Secretary Sajid Javid in June.
Assange received a 50-week sentence in Belmarsh Prison, southeast London, after being found guilty of breaching the Bail Act in April.
He was arrested at the Ecuadorian Embassy, where he took refuge in 2012 to avoid extradition to Sweden over sexual assault allegations - which he has denied.
District judge Vanessa Baraitser on Friday told Assange, who appeared by video-link: "You have been produced today because your sentence of imprisonment is about to come to an end.
"When that happens your remand status changes from a serving prisoner to a person facing extradition.
"Therefore I have given your lawyer an opportunity to make an application for bail on your behalf and she has declined to do so. Perhaps not surprisingly in light of your history of absconding in these proceedings," she said.
"In my view I have substantial ground for believing if I release you, you will abscond again," the judge added.
Assange was asked if he understood what was happening, and replied: "Not really. I'm sure the lawyers will explain it."
He faces 18 charges in the US, including computer misuse and the unauthorized disclosure of national defence information. He is also accused of working with former US Army intelligence analyst Chelsea Manning in "unlawfully obtaining and disclosing classified documents related to the national defence", according to the US Justice Department.
Assange spent seven years inside the Ecuadorian embassy in London before being handed over to British authorities by Ecuador in April.
In May, Swedish prosecutors reopened their investigation into an allegation of rape against Assange.
( With inputs from IANS )