The ex-president's widow, Mirjana Markovic, and son, Marko Milosevic, are wanted in Serbia for heading a cigarette smuggling ring in the early 1990s, which investigators said netted them several million dollars. The mother and son, who have lived in Moscow for the last few years, have denied the allegations, but have refused to return to the country to face charges.
"Taking into account that Milosevic and Markovic were granted political asylum in Russia, the justice minister decided to send a request for their extradition," the ministry said in a statement.
Serbian media first circulated reports in February on Russia granting political asylum to Markovic and Marko Milosevic, but the Russian Foreign Ministry said at the time it was unable to confirm or deny reports.
However, Konstantin Poltoranin, a spokesman for the Russian Federal Migration Service, said that refugee status had been granted to Markovic and Milosevic in March 2006 in accordance with a UN convention.
Markovic was also accused in 2002 of abuse of power for giving a state apartment to her grandchild's nanny. Marko Milosevic also faced charges, which were later dropped, of threatening to kill an opposition youth group member in 2001.
Slobodan Milosevic, who led Yugoslavia into war and international isolation, culminating in the NATO bombing of the country in 1999, died in custody at The Hague in March 2006, before a UN war crimes tribunal passed a verdict on his role in the wars in Croatia, Bosnia and Kosovo in the 1990s.
He was reported to have died of a heart attack. He had repeatedly complained of high blood pressure and chest pains asking for permission to undergo treatment in Moscow, which was denied.
Milosevic's brother, Borislav, who was the Yugoslavian ambassador to Russia, also lives in Moscow.