It was not clear whether he intended to go into exile permanently or was simply leaving Yugoslavia for a limited period while the new political leadership settled in.
Marko Milosevic was seen at Belgrade airport with his wife and son on Saturday morning, hours after his father's admission of defeat in the presidential elections.
However the Yugoslav embassy in Moscow dismissed reports of his flight as "just a rumour", and said it had no information about his possible arrival.
Correspondents say the young Mr Milosevic, a highly controversial figure hated by his father's political opponents, has an extensive business empire which is reputed to have made him very wealthy.
Businesses ransacked
An airline pilot told Reuters news agency: "This morning at 0840 a.m. (0640 GMT) Marko Milosevic and his wife and child, left Yugoslavia in a JAT (Yugoslav Airlines) plane, he left for Moscow".
It was not clear whether he intended to go into exile permanently or was simply leaving Yugoslavia for a limited period while the new political leadership settled in.
Slobodan Milosevic said in a television broadcast on Friday that he now looked forward to resting a bit and spending more time with his grandson, also called Marko.
"Given the end of this huge responsibility which I carried for a whole decade, I intend to rest a bit, to spend more time with my family, especially with my grandson Marko, and then continue to strengthen my party," Milosevic said.
Marko Milosevic is reported to own an amusement complex in his father's home town of Pozarevac, which was ransacked during the recent protests.
His business interests are also believed to include a bakery, a store selling computer equipment, a disco club and a luxurious perfume shop in central Belgrade, named Scandal, which was also looted by rampaging protesters on Thursday.