Five men were arrested near Athens and a sixth in the northwestern city of Ioannina, and police found petrol bombs at the home of one of them near Athens, the source said.
Police have not yet confirmed that the men are members of the Greek neo-Nazi party Golden Dawn but said they belonged to far-right groups.
There has been a spate of far-right violence against migrants and left-wing activists in Greece recently.
Among those wounded -- two of whom were taken to hospital -- was a lawyer representing the family of Pavlos Fyssas, the anti-fascist rapper killed by Golden Dawn members in September 2013, according to police sources.
According to the Facebook page of the Favela Free Social Centre that was attacked, the perpetrators were "Golden Dawn members with iron bars, helmets and flares".
A total of 70 Golden Dawn lawmakers and party officials are on trial on a wide range of charges, including membership of a criminal organisation linked to the fatal stabbing of Fyssas.
The Favela centre was also attacked last August, and four people were arrested by the counter-terrorism unit in January.
During the searches of their homes, police found posters of neo-Nazi propaganda and training weapons.
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