The police move came after Golden Dawn party members last week smashed stalls at a church fair in Rafina near Athens and at a farmers' market in the central Greek town of Messolonghi.
Videos of the attacks posted by the media on the Internet showed gangs of men dressed in boots, black shirts and carrying Greek flags smashing the stalls in the presence of Golden Dawn members of parliament.
The party said it had organized the attacks. It also said it would take legal action against the police for "interrupting the free operation of our offices."
The local police chief in Rafina was suspended pending the results of a government inquiry. No police were seen in any of the videos.
Golden Dawn, which political opponents brand as being neo-Nazi, has soared in popularity as Greece sinks deeper into a debt-fueled morass. The party won nearly 7 percent of the vote in June's election and 18 seats in the country's 300-member parliament.
Its support has climbed to 12 percent, according to an opinion poll published last week.
The party rejects repeated allegations made by immigrant and human rights groups that it is linked to a sharp recent increase in racist attacks.
Also Monday, Greek's public order ministry withdrew police guards who were protecting Golden Dawn lawmakers, saying it didn't want the guards to face a conflict of interest between protecting officials and having to stop them from breaking the law.