The detention comes at a sensitive time, with the United States taking a leading role in efforts to secure tough international sanctions on North Korea over its latest nuclear test.
Pyongyang has a history of using foreign detainees as bargaining chips to extract concessions and high-profile visits to secure their release.
The student, identified as Otto Frederick Warmbier from the University of Virginia, had entered North Korea as a tourist "for the purpose of bringing down the foundation of its single-minded unity at the tacit connivance of the US government and under its manipulation," the North's official KCNA news agency said.
China-based Young Pioneer Tours, which organises regular trips to North Korea, said Warmbier had been a member of a New Year tour and was arrested when the group was set to return to Beijing on January 2.
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"We hope his release can be secured as soon as possible," the tour group said, adding that it was assisting the US State Department in the affair.
State Department spokesman John Kirby, citing "privacy considerations," declined to comment beyond acknowledging the reports of Warmbier's arrest and stressing that the welfare of US citizens was always a top priority.
Warmbier becomes the third North American detained in North Korea, which last month sentenced a 60-year-old Canadian pastor to life imprisonment with hard labour on sedition charges.
During a recent interview that the pastor, Hyeon Soo Lim, gave to CNN in Pyongyang, the North presented another ethnic Korean prisoner, whom they said was a US citizen arrested for spying in October.
The term "hostile act" is a catch-all accusation that has been levelled at numerous detained foreigners in the past -- covering a range of possible charges from espionage to illicit missionary work.