The CNBC broadcaster reported that the lawsuit was filed on Thursday.
It reportedly challenges a provision of the National Defense Authorization Act, which bars Huawei and another Chinese IT company, ZTE, from participating in US government procurement.
The US authorities have been citing security threats, suggesting that Huawei might gather intelligence and pass it to the Chinese government, something denied by the company.
The company has recently been accused by the United States, as well as a number of other countries, of stealing commercial information. Previously, Huawei Chief Financial Officer Meng Wanzhou was arrested in Vancouver last December at the United States' request, reportedly on suspicions of failing to comply with US sanctions against Iran. The arrest was decried by Beijing, which demanded that Canadian authorities immediately release the Chinese national. The hi-tech company has insisted Meng has done nothing illegal.