Mr Trump's executive order prohibits transactions with TikTok's owner ByteDance from mid-September.
Officials in Washington are concerned that the company could pass data on American users to the Chinese government, something ByteDance has denied doing.
The short video-sharing app has 80 million active US users.
TikTok says it has tried to engage with Mr Trump's administration for nearly a year but has encountered a lack of due process and an administration that pays "no attention to facts".
"To ensure that the rule of law is not discarded and that our company and users are treated fairly, we have no choice but to challenge the executive order through the judicial system," a company spokesperson said.
TikTok expects the legal action to begin this week, says BBC Business reporter Vivienne Nunis.
On Friday a group of Chinese-Americans filed a separate lawsuit against the president's similar ban on the social media app WeChat, which is owned by the Chinese firm, Tencent.