The complaint, filed in Plano, Texas, the headquarters of Huawei's US operations, cites the framers of the US Constitution, including Alexander Hamilton and James Madison, in arguing that the law in question violates the constitutional separation of powers, denies due process and amounts to a "Bill of Attainder" that singles out a specific entity for adverse treatment.
Guo added the company was seeking unspecified damages.
Federal judges will also have to consider whether the ban violates Huawei's fundamental rights, Ku said, but "doing business with the US government doesn't seem to be a fundamental right, and there are reasonable grounds for Congress to act against Huawei".
Guo also said the USA government "has hacked our servers and stolen our emails and source code", without providing details.
The Chinese telecoms firm manufactures a range of technology, from network equipment to mobile phones.
It comes as the biggest global maker of network equipment fights a USA campaign to persuade allies to shun Huawei. Prosecutors allege that Skycom is a hidden subsidiary of Huawei, while Huawei maintains they are two independent companies.
The ban came into effect last August as part of the Defense Authorization Act, which also placed similar restrictions on fellow Shenzhen-based telecoms equipment company ZTE.
He said Beijing had issued an official protest against the defence bill's "negative content concerning China".
He also claimed that USA government agencies "had hacked" Huawei "servers and stolen emails and source code".
This comes just as the world readies for the roll-out of ultra-fast 5G telecommunications, an advancement in which Huawei will play a key role and which will allow widespread adoption of next-generation technologies like artificial intelligence.
The firm has responded to the pressure with an aggressive PR campaign in recent months, with Ren, its reclusive founder, denying the claims in several foreign media interviews.
The charm offensive went into another gear Wednesday as Huawei welcomed news organisations on a tightly guarded tour of its massive production lines and research and development facilities in southern Guangdong province.
Guo suggested the USA campaign to contain Huawei was prompted in part by the US's belated realisation that the company had become a rival to American tech leaders.
China's government arrested two Canadians, a former diplomat and a businessman, on December 10 in what was widely seen as an attempt to pressure Canada to release Meng, the company's CFO.
Huawei has repeatedly insisted that it can not be coerced by the Chinese government to install backdoors, spy on its customers, or hand over data.
The ban is "based on numerous false, unproven and untested propositions", said Song Liuping, the company's chief legal officer, at the news conference.
According to the United States, equipment manufactured by Huawei is highly likely to be exploited by the Chinese Communist government in order to keep other countries under surveillance and interfere with crucial communications.
The decision by China's leading telecom company is the latest chapter in the ongoing battle with Washington.
Some legal experts, however, said Huawei's lawsuit is likely to be dismissed because US courts are reluctant to second-guess national security determinations by other branches of government.
Guo later said the United States wanted to thwart Huawei's rise as it "hampers U.S. efforts to spy on whomever it wants".
The restrictions are particularly hurting Huawei's rollout of 5G in the United States, which could reduce the cost of wireless infrastructure by between 15% and 40%.