The FSB said the American had been detained on December 28 but it gave no details of the nature of his alleged espionage, Reuters reported.
The English-language service of TASS news agency named the American as Paul Whelan but Reuters was unable to independently confirm the exact spelling of his name.
Russia’s Foreign Ministry told TASS it could not provide further detail on the case, but said the US Embassy in Moscow had been informed.
The US Embassy would not comment directly but referred reporters’ inquiries to the press office of the State Department in Washington.
Under Russian law, espionage can carry between 10 and 20 years in prison.
Earlier this month Russian national Maria Butina pleaded guilty in a US court to a conspiracy charge in a deal with prosecutors, and admitted to working with a top Russian official to infiltrate American conservative activist groups and politicians as an agent for Moscow.
Russia’s relations with the United States plummeted when Crimea reunified with Russia in 2014 and Washington and Western allies have imposed a broad range of sanctions on Russian officials, companies and banks.