The North's state-run KCNA news agency said the student, Otto Frederick Warmbier, entered North Korea as a tourist and "was caught committing a hostile act against the state", which it said was "tolerated and manipulated by the U.S. government".
KCNA said Warmbier had entered the country with an "aim to destroy the country's unity". It did not elaborate.
Warmbier is an undergraduate at the University of Virginia, according to the university's website. Gareth Johnson of China-based Young Pioneer Tours confirmed Warmbier was on one of its tours and said he had been detained in North Korea on Jan. 2.
An official at the U.S. embassy in the South Korean capital Seoul said it was aware of the reported arrest. Johnson said Young Pioneer Tours was in touch with Warmbier's family and U.S. officials.
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"We are in touch with Otto's family, the U.S. State Department and the Embassy of Sweden in Pyongyang and doing all we can to secure his release," Johnson told Reuters.
The Swedish Embassy represents U.S. interests in North Korea.
A South Korean-born Canadian pastor was arrested in North Korea last year and given a life sentence for subversion.
Earlier this month, a Korean-American man told CNN in Pyongyang that he was being held by the state for spying.
In 2014, Pyongyang released three detained Americans. Last October, it freed a South Korean national with a U.S. green card after holding him for six months.
South Korea warned that the United States and its allies were working on further sanctions to inflict "bone-numbing pain" on North Korea after its latest nuclear test this month, in contravention of U.N. Security Council resolutions, and urged China to do its part to rein in its neighbour.
