A local news source, the Athens News Agency, said police made 10 arrests.
Earlier, 3,000 people gathered at a rally in Syntagma Square protesting against police violence.
Called by anarchists, the demo prompted Greek authorities to go high alert, deploying 5,000 officers.
Earlier Sunday, clashes before dawn erupted between police and youths in the neighbourhood of Exarcheia, leaving a Portuguese tourist lightly injured after he was hit on the head by a stone.
Exarcheia is a popular meeting point for anarchists and the place where 15-year-old Alexis Grigoropoulos was shot dead by police on December 6, 2008 sparking weeks of riots.
Last year`s demonstrations descended into violence with 12 police officers injured and more than 200 people arrested.
This year`s anniversary was preceded by a statement issued by Grigoropoulos` friend, Nikos Romanos, who is in jail for armed robbery he committed to finance his anarchist group.
Romanos called all anarchists to declare war against the state and middle class, in what he called a "Black December" of "blood and fire".
Greece is in the grip of deep economic recession, with the country divided over austerity measures and reforms implemented by the leftwing SYRIZA government to meet conditions for an international bailout.
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