The law was passed with support from both Republicans and Democrats in Congress and was upheld unanimously by Supreme Court justices earlier this week.
The issue exposes a rift on a key national security issues between the president-elect and members of his own party. His pick for Secretary of State, Marco Rubio, had vocally supported the ban.
"TikTok extended the Chinese Communist Party's power and influence into our own nation, right under our noses," he said last April. But he seemed to defer to the president-elect when a journalist asked if he supported Trump's efforts to restore the ban.
"If I'm confirmed as secretary of State, I'll work for the president," he told Punchbowl media last week.
After Trump intervened on Sunday morning, Senate Intelligence Committee Chair Tom Cotton, a Republican senator from Arkansas, broke with Trump by saying that any company that helps TikTok stay online would be breaking the law.
"Any company that hosts, distributes, services, or otherwise facilitates communist-controlled TikTok could face hundreds of billions of dollars of ruinous liability under the law, not just from DOJ, but also under securities law, shareholder lawsuits, and state AGs," he wrote on social media.
An executive order that goes against the law could be fought in court.
Several states have also sued the platform, opening up the possibility to TikTok being banned by local jurisdictions, even if it is available nationally.
Although the platform went live again on Sunday for existing users, the question of whether third-parties - hosting platforms or app stores like Google or Apple - could support TikTok in the US remains murky, says University of Richmond law professor Carl Tobias. The app had been removed from those stores in anticipation of the ban.
"It is murky," he told the BBC.
In a post on Truth media, Trump promised to shield companies from liability, opening the door to TikTok being available on Apple and Google again.
"The order will also confirm that there will be no liability for any company that helped keep TikTok from going dark before my order," the president-elect said on Truth Social Sunday.
But during the Supreme Court hearings, Solicitor General Elizabeth Prelogar was adamant that an executive order cannot change the law retroactively.
"Whatever the new president does, doesn't change that reality for these companies," Justice Sonia Sotomayor said during the hearings.
"That's right," Prelogar said.
Professor Tobias said that the law does include a provision that would allow the president to postpone the ban for up to 90 days, if he can show that the company is making substantial progress on alleviating national security issues. But, he said, it's not clear whether those conditions have been met.
"The best thing Trump could do is work with Congress, and not potentially be in violation of the law or have any questions left hanging," he said.
"I don't know that we're going to know a whole lot more until we see that executive order."