The ANA news agency reported that at least three men entered the embassy and waved the flag, which was hanging from the roof of the building. Police intervened and the three men were detained, the source added.
A man was seen on the balcony of the embassy holding a portrait of Assad and shouting "dictator".
Syrians who fled to Greece when Hafez Assad's regime was installed in 1970 came to the building to celebrate.
"The dictator fled, it's all over ... a new dawn is breaking for Syria," said Maarouf Alobeid, a cardiologist who has lived in Greece for four decades.
"I came fleeing from my home...the thirst of the Syrian people for freedom, for democracy cannot be described," he added.
"Twenty-four million Syrians don't sleep at night," said Nader Halbouni, a Syrian community leader in Greece.
A Syrian rally is planned for later on 8 December.
Tens of thousands of Syrians fled to Greece during the 2015 migration crisis, most of them aiming to reach Germany and other EU member states.
According to the Ministry of Immigration, more than 15,000 Syrians currently hold residence permits in Greece. | BGNES
