" Ecuador is studying and analysing the request," Foreign Minister Ricardo Patino told reporters in Quito.
The Foreign Office says it will work with Ecuador to resolve the situation.
Mr Assange could still take his case against extradition to the ECHR and has until 28 June to make the move, or extradition proceedings will begin.
Swedish prosecutors want to question him over allegations of rape and sexual assault made by two female former Wikileaks volunteers in mid-2010 but has not filed any charges.
Mr Assange, whose Wikileaks website has published a mass of leaked diplomatic cables that embarrassed several governments and international businesses, claims the sex was consensual.
In a statement, Ecuador's embassy said he had arrived there on Tuesday afternoon to seek asylum.
"As a signatory to the United Nations Universal Declaration for Human Rights, with an obligation to review all applications for asylum, we have immediately passed his application on to the relevant department in Quito," it said.
"While the department assesses Mr Assange's application, Mr Assange will remain at the embassy, under the protection of the Ecuadorean government."