The trouble came as Barack Obama visits Athens on his final state tour as President of the United States
. He gave a speech Wednesday
after touring the Acropolis, the complex of monuments known as the "cradle of democracy," in which he said democracy was "complicated" and "messy" but designed to correct mistakes.
The arrests occurred Tuesday after a peaceful demonstration, organized by the Communist Party and permitted by police, in Omonia Square near central Athens.
About 5,000 people attended the anti-establishment protest, police said. After it was over, a group of some 100 to 150 anarchists became violent, police said.
Unrest broke out as the group tried to break through a police cordon to march to the US Embassy and Presidential Mansion, where Obama was attending an official state dinner.
Protesters threw Molotov cocktails, and police responded with stun grenades and tear gas, dispersing the crowds who eventually retreated into the side streets.
Three officers suffered minor injuries, police said.
Obama warns of 'crude nationalism'
On Tuesday, Obama gave a news conference alongside Greek Prime Minister Alexis Tsipras in which he warned against "crude nationalism"
in the wake of Donald Trump's victory in the US presidential election last week.
Obama said countries across Europe as well as the United States were confronting populist movements based on a fear of intruding global forces, arguing people "are less certain of their national identities or their place in the world."
He said leaders should heed lessons from election results in the United States and in Britain, which voted in June to exit the European Union.
Obama is on a weeklong, three-stop foreign trip that will also take him to Germany and Peru.