In a court document seen by Reuters, she said there were no further avenues to pursue to take the investigation forward.
He has been living at the Ecuadorian Embassy in London since 2012, where he sought refuge as he feared he would be arrested in Sweden on the rape charge and extradited to the USA as he is wanted for revealing secret government documents.
He sought asylum at the embassy over fears that if he is extradited to Sweden he would be sent onward to the US for prosecution over WikiLeaks' publication of secret documents, including thousands of USA diplomatic cables.
Assange, 45, took refuge in Ecuador's embassy in London in 2012 to escape extradition to Sweden to answer questions about sex-crime allegations from two women.
"The UK has refused to confirm or deny whether it has already received a USA extradition warrant for Julian Assange". She said prosecutors had been unable to make a full assessment of the case and were not making a finding on whether Assange was guilty of the allegations.
The UN had called on Swedish and British authorities to free Mr Assange from "arbitrary detention" in a report released past year, with the United Kingdom failing to overturn the findings on appeal.
CIA Director Mike Pompeo last month called WikiLeaks a "hostile intelligence service", and Attorney General Jeff Sessions, responding to a question about Assange, said the administration was stepping up its efforts against all leaks of sensitive information.
U.S. President Donald Trump said last month he would support any decision by the Justice Department to charge Assange.
Assange is wanted by British police for extradition to Sweden.
However, it noted that now the Swedish authorities had dropped their investigation, Assange was "wanted for a much less serious offence" than before and said the force would "provide a level of resourcing which is proportionate to that offence".
Julian Assange's Swedish lawyer Per E. Samuelson says it is a "day of victory" for the WikiLeaks founder after Sweden's top prosecutor dropped an investigation into a rape claim against him. United Kingdom government offices referred comment on Mr Assange's case to the police. "Focus now moves to United Kingdom".
The sun-starved WikiLeaks provocateur, looking healthy if pale, emerged Friday afternoon to address the media in the open air of the embassy's balcony.
The letter argued that recent public declarations constituted an "obvious risk" for Mr Assange, who originally faced three sexual assault charges that he denied.
British officials said they do not comment on individual extradition cases.
Ecuador's foreign minister, Guillaume Long, tweeted Friday that Britain "must now grant safe passage" to Assange.
Assange and WikiLeaks have repeatedly infuriated USA officials with the widespread release of sensitive secret documents related to military operations in Afghanistan and Iraq and diplomatic relations around the world.
Ms Ny said the motive for her decision was that there is no reason to believe the decision to surrender Mr Assange to Sweden can be executed in the foreseeable future. It is not clear if that may change now that the investigation has been dropped.
WikiLeaks played a central role in the 2016 presidential race when it published emails stolen through hacking the Democratic National Committee and later from John Podesta, chairman of Hillary Clinton's campaign.
Army Pvt. Chelsea Manning served seven years in prison for giving classified material to WikiLeaks.
Assange has said the sex was consensual.
Towards the end of his presidency, Barack Obama decided she should be freed and the former intelligence analyst was recently released from jail.
British police kept up round-the-clock guard outside the embassy until December 2015, when the operation was scaled back, in part because of the cost, which had exceeded 11 million pounds (over $17.5 million at the time).