A notice from the Harbin police headquarters named them as Katheryn A Wilson, Robert J Snelling and Stephen W Johnson and said they worked through the National Security Agency.
The police said nothing about how they obtained the names or where the three were believed to be at present.
The alleged attacks targeted the systems for managing the Games themselves, such as registration, competition entry and travel, all of which stored "vast amounts of sensitive personal data of individuals associated with the Games", the police said.
The attacks continued during the Games in an attempt to "disrupt them and undermine their normal operations", according to the official Xinhua News Agency.
The report also alleged the NSA cyberattacks targeted critical infrastructure in Heilongjiang province, which includes Harbin, such as energy, transportation, water resources, telecommunications, and defence research institutions.
The hackers also attacked Chinese technology company Huawei, Xinhua said.
The report alleged the NSA "transmitted unknown encrypted data packets to specific devices running Microsoft Windows operating systems within the province".
Chinese foreign ministry spokesman Lin Jian dished out further criticisms at a daily briefing, while offering no firm evidence.
The attacks caused "serious harm to China's critical infrastructure, national defence, finance, society, production, and the personal information security of Chinese citizens. The nature of these actions is extremely malicious," Lin said.
The US embassy in Beijing did not immediately respond to messages seeking comment.
It is not clear why the alleged attacks would have been timed to the Asian Games, unless it was expected that China might ease some of its strict internet controls while hosting the competition.
The US and China have long accused each other of cyberattacks, with the US also naming Chinese individuals who worked for military hacking units, even issuing wanted posters for them.
The Office of the Director of National Intelligence in March called China "the most active and persistent cyber threat to US government, private sector and critical infrastructure networks".
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