Widely circulated videos appeared to show peaceful protestors being thrown to the ground and attacked with batons on Sunday.
ADVERTISEMENTGreek authorities have launched an investigation into allegations of police violence after clashes in Athens.
Widely circulated videos on social media appear to show police carrying out the violent arrest in a suburb of the Greek capital.
Images from Sunday showed a young man being beaten to the ground with a baton by a police officer, as at least three other officers stood nearby.
The man can be heard shouting "it hurts", while passers-by express outrage.
The Athens public prosecutor's office ordered a preliminary investigation on Monday to "examine possible criminal acts perpetrated by police officers".
The police have also ordered an internal investigation into the matter.
According to a police statement, the officers were carrying out checks at Nea Smyrni Square to enforce COVID-19 restrictions and limit the spread of the coronavirus.
Greece has recorded 6,758 deaths from COVID-19 since the start of the pandemic, with more than half in the last three months. The country has been under a strict second lockdown since November 7.
Police say they had received "a number of complaints" the restrictions were being violated in Nea Smyrni Square.
"During the checks, the police team was, unprovoked, attacked by a group of 30 people, resulting in the injury of two police officers," the statement continued.
Eleven people were arrested from the group that "attacked" the police officers, it added.
Following the clashes, hundreds of people gathered in the square on Sunday evening to demonstrate against "police violence". The protest was dispersed by riot police using tear gas and stun grenades.
The incident has generated an outcry from many politicians in Greece, including former Prime Minister Alexis Tsipras.
"The unprovoked attack of police on families and young children in Nea Smyrni Square ... is the drop that overflows the glass," the leader of the opposition Syriza party wrote on Facebook.
"The country has a government that has completely lost control of the pandemic and only knows how to weigh in."
A spokeswoman for the government, Aristotelia Peloni, responded that the executive is trying "to get the country out of this unprecedented health crisis with as few casualties as possible".
"Unfortunately, the opposition is exploiting the tensions and inflaming the political and social climate," Peloni added.