After leaking information about the National Security Agency's surveillance programme to the Guardian newspaper, he said he chose Hong Kong because the city has "a spirited commitment to free speech and the right of political dissent".
Mr Snowden's current whereabouts cannot be confirmed. He left the hotel he had been staying in shortly after going public.
The Hong Kong government has promised to handle any extradition request from the US according to established law and policy.
Hong Kong signed an extradition treaty with the US shortly before the territory returned to Chinese sovereignty in 1997.
"You get extraditions several times a year from Hong Kong," Clive Grossman S.C, a barrister and former vice-chairman of the Hong Kong Bar Association, told the BBC.
Under the Fugitive Offenders (United States of America) Order, both Hong Kong and the US have agreed to extradite someone who has committed "an offence which is punishable under the laws of both Parties by imprisonment or other form of detention for more than one year... unless surrender for such offence is prohibited by the laws of the requested Party."
Regina Ip, a legislator and Hong Kong's former Secretary for Security, told reporters in May that the Hong Kong government was "obliged to comply with the terms of agreements" with the US government, including extradition treaties.
"It's actually in his best interest to leave Hong Kong," she said, referring to Mr Snowden.
However, the extradition process can be a long and complicated one in sensitive cases like this, Tim Parker, an immigration lawyer based in Hong Kong, has told the BBC.
"There are a number of hurdles that could come up for the extraditing authority, to the advantage of Snowden," he said.
"There is a bar under Hong Kong's extradition law... to extradition for an offence that is of a political character, [where] the prosecution is thought not just to be the application of the criminal law, but to crush that person or to crush their dissent," Mr Parker said.
Another potential hurdle would be any intervention from Beijing, which could block an extradition if it raised questions "going to their national security, foreign affairs, or defence", Mr Parker says.
A handover could also be halted if Mr Snowden was believed to be in danger of receiving inhumane treatment in the US, Mr Parker added.
"If Mr Snowden is at risk of being detained under the sort of conditions that Bradley Manning has reportedly been detained, which the UN special rapporteurs have said amounted to cruel, inhumane or degrading treatment or punishment... then Hong Kong would not be allowed under its law, and could not extradite him to the US."
A further consideration is what visa Mr Snowden used to enter Hong Kong. If his visa is due to expire soon, a formal extradition request may not be needed.
However, it would not be "legally possible" under Hong Kong law for Mr Snowden to be forcibly taken to Beijing, Mr Parker says.
"That would be a serious breach of the autonomy under Hong Kong's One Country Two Systems arrangement. There aren't really any known cases of that having been done off the books [either]," he says.
Edward Snowden, who has been charged with espionage by US over leaks about US surveillance programmes, is thought to have been in Hong Kong since 20 May.