US security officials have expressed concern that the app, owned by Chinese firm ByteDance, could be used to collect the personal data of Americans.
TikTok has denied accusations that it is controlled by or shares data with the Chinese government.
The fast-growing app has up to 80 million active monthly users in America and the ban would be a major blow for ByteDance.
“As far as TikTok is concerned, we’re banning them from the United States,” Mr Trump told reporters aboard Air Force One.
It was not immediately clear what authority Mr Trump has to ban TikTok, how that ban would be enforced and what legal challenges it would face.