The Federal Security Service (FSB), the successor to the dreaded Soviet KGB, said that the woman, a second secretary at the US embassy, had been detained briefly on Monday after she was "caught red-handed while conducting an espionage operation".
In official statements, the FSB referred to her only as "the diplomat" but Interfax news agency, which identified her as 33-year-old Cheri Leberknight, said that information had come from the security service.
The Americans, who received an official Russian protest about the matter, did not immediately comment.
Alexander Zdanovich, the FSB spokesman, said "the diplomat" worked for the CIA and had been caught while "trying to obtain secret documents of a military-strategic nature from a Russian citizen". She was carrying a map, invisible ink tablets and radio interception equipment that "proved she was a spy".
She was taken to the FSB's reception centre, where Russian Foreign Ministry officials made a "resolute protest" in the presence of the US consul. She was then released, the FSB said, adding that her future would be decided through diplomatic channels.
Ms Leberknight could have been set up by the "Russian citizen" working on Moscow's behalf. Such are the games that secret services routinely play. If she was reporting to the CIA, then the Americans might quietly withdraw her to avoid an expulsion scandal.
Playing to the gallery, Russia's Foreign Minister, Igor Ivanov, said the episode "hardly promotes an improvement in the climate of [US-Russian] relations". However, when he spoke by telephone to the US Secretary of State, Madeleine Albright, he did not even mention the incident, Interfax said.
Moscow apparently wanted to give the West a little frisson to remind it of the Cold War, without sending temperatures dangerously low. The independent channel, NTV, suggested Moscow was reacting to the arrest in the US of Daniel King, who worked for the US navy for 18 years. He had been charged and was in custody, NTV said. He was said to have confessed to taking a computer disc with secrets to the Russian embassy in Washington. The FSB cautioned journalists against linking the two cases, saying: "We do not work on the old Cold War principle of `an eye for an eye'."
Relations between Russia and the West are certainly tenser now than ever since the fall of the Berlin Wall 10 years ago. Disappointed by the failure of their economic reforms, Russians are in a mood of self-loathing that can be expressed as resentment against the West.
Russia was extremely offended when Nato ignored its protests at the bombing of Yugoslavia earlier this year. Now, as Moscow resorts to force in Chechnya, it is angered by "double standards" as Western politicians call for a political solution. Moscow and Washington are also arguing over changes America would like to make to a missile defence treaty.
And yet as Leonid Kolosov, a retired KGB agent who spied for Moscow during the Cold War, said yesterday, the latest scandal was like a nip of frost in spring rather than deep mid-winter. The mock outrage was funny because spying was the "world's oldest profession" and the "game" would always go on.