The announcement was made while U.S. President Barack Obama was visiting South Korea, one of Washington's closest allies and still technically at war with Pyongyang.
"A relevant organ of the DPRK put in custody American Miller Matthew Todd on April 10 for his rash behaviour in the course of going through formalities for entry into the DPRK to tour it," North Korea's KCNA news agency said, using the country's official name, the Democratic People's Republic of Korea.
KCNA said the detained man had a tourist visa for the DPRK, but tore it to pieces and shouted that he had come "to the DPRK after choosing it as a shelter."
Uri Tours, a New York-based travel agency that specialises in trips to North Korea, identified the tourist as Matthew Miller, and said in a statement on their website that he had been visiting the country on a private tour.
"We are doing all we can to assist Mr. Miller through this process," the statement said, adding that the tour agency had been working with "diplomatic entities" to try and secure Miller's release.
The U.S. State Department said it was aware of reports that a U.S. citizen had been detained in North Korea and it was in touch with the Swedish Embassy in Pyongyang on the issue.
"We don't have additional information to share at this time," U.S. State Department spokeswoman Jen Psaki told a regular news briefing.
The United States has no diplomatic relations with North Korea and the interests of its citizens in the country are represented by Sweden.
Kenneth Bae, a Korean American missionary, has been held in North Korea for more than a year. He was arrested as he led a tour group in the country in 2012 and sentenced to 15 years of hard labor on charges of state subversion.
North Korea has twice cancelled visits by Robert King, the U.S. special envoy for North Korean human rights issues, to discuss Bae's case.
Bae has acknowledged conducting religious services in North Korea, one of the world's most isolated states and long hostile to Westerners advocating religious causes.
Psaki said Swedish diplomats had visited Bae on April 18 and the United States remained "deeply concerned" about his health.
"We continue to urge North Korean authorities to grant Mr. Bae a special amnesty and immediate release on humanitarian grounds," she said.
Bae's family says he suffers from a variety of health issues, including diabetes, an enlarged heart, kidney stones and severe back pain.
Last month, North Korea freed John Short, a 75-year-old Australian missionary it had arrested in February.
Short was accused by Pyongyang of committing a crime by distributing bible tracts at a Buddhist temple in Pyongyang on the birthday of former North Korean leader Kim Jong Il.
North Korea said it had decided to deport Short, partly in consideration of his age, and issued what it said was a picture of a handwritten note from him apologizing for his act.
Obama said on Friday that North Korea represented a threat not just to Asia but to the United States. He and South Korea's President Park Geun-hye said they would respond firmly to any "provocations".