An airport official said the body would remain there overnight. It was not clear when and where it would be flown out.
Milosevic died on March 11 while in custody at the war crimes tribunal in The Hague.
A Serbian court today said Milosevic's widow, Mirjana Markovic, would not be arrested if she returned to Serbia from Russia. But it said Markovic will face a court hearing and her passport will be confiscated.
Serbia's government said the decision meant the funeral could take place in the country.
However, the government has ruled out a state funeral.
Milosevic's son, Marko, had said he might consider a burial in Moscow unless he could be sure his mother would be safe in Belgrade.
Milosevic's family has accused the UN tribunal of murdering the former Serb strongman by refusing his request to travel to Russia for medical treatment.
The UN court that has been trying Milosevic for more than four years today formally closed his trial for war crimes, genocide, and crimes against humanity.
(compiled from agency reports)