The Israeli is suspected of involvement in training militants for drug cartels in Colombia in the late 1980s, according to the Interfax and RIA-Novosti news agencies and Channel One television, which cited unidentified law enforcement officials.
The Moscow air and water transport police confirmed that an Israeli was recently detained at the capital's Domodedovo airport, but declined to provide details.
Interfax and Channel One said the man's last name was Klein but gave different first names.
In April, Interpol issued an international arrest warrant for Yair Klein, a former lieutenant colonel in the Israeli army, and two other Israelis accused of training private armies of Colombian drug cartels and right-wing death squads. They face nearly 11 years in prison if convicted on charges of criminal conspiracy and instruction in terrorism, Colombia's domestic intelligence agency said at the time.
It was not immediately clear whether the man detained in Moscow was Yair Klein.
Yair Klein and the other two Israelis are accused of helping set up training camps to teach private armies working for Colombian drug lords Pablo Escobar and Gonzalo Rodriguez Gacha about explosives, car bombs and high-profile killings. The armies later morphed into Colombia's right-wing death squads.
Austria does not intend to expel Russian diplomats because of the spy scandal