The five users seek to block the law, which makes the social network illegal and prevents Google and Apple app stores from offering it in the state.
The videos app is used by more than 150 million Americans.
The lawsuit names Montana Attorney General Austin Knudsen. TikTok users argue that the state seeks to “exercise an authority over national security that Montana does not have and prohibit free speech.” The legal action added that users consider that the law violates their constitutional rights.
Knudsen did not immediately comment.
“Montana can’t ban its residents from viewing or posting on TikTok the same way you could ban the Wall Street Journal because of who owns it or because of the ideas it spreads,” he said.
The lawsuit is assigned to Judge Donald Molloy, who was nominated for the post by former President Bill Clinton, a Democrat, in 1995.
The short video network, owned by Chinese technology company ByteDance, said the Montana ban “infringes the First Amendment (Constitutional) rights of the people of Montana.”
TikTok has faced numerous calls from US lawmakers and state officials to ban the app in the country due to concerns about possible Chinese government influence on the platform.
Gianforte, a Republican, said the law would advance “our shared priority of protecting Montanans from surveillance by the Chinese Communist Party.”
TikTok has repeatedly denied sharing data with the Chinese government and has said the company would not do so if asked.
Montana, which has a population of just over 1 million people, said TikTok could face fines of up to $10,000 a day if it fails to comply with the ban.
The American Civil Liberties Union (ACLU) criticized the law, calling it “unconstitutional.”