MOSCOW—Russian authorities expelled an American they accused of being a Central Intelligence Agency officer operating under diplomatic cover on Tuesday, posing a new potential setback to recent U.S. efforts to rebuild frayed ties with Moscow.

In an episode that appeared more costume party than spy thriller, Russian authorities detained American Ryan C. Fogle near a Moscow park late Monday, according to Russia's spy service—which said he was wearing a dirty-blond wig and carrying "special technical equipment" as...