Ilias Kasidiaris, who was elected to Greece’s parliament in last month’s elections, was debating with two female politicians on a chat show.
Video footage shows him throwing a glass of water at one of the women.
When the other intervened, he slapped her in the face three times.
Ilias Kasidiaris appeared to have been provoked when Rena Dourou of the radical left-wing Syriza party mentioned his alleged involvement in an armed robbery in 2007.
He jumped up and threw a glass of water across the table at her, a YouTube clip of the Antenna television channel showed.
When Liana Kanelli of the Greek Communist party, the KKE, apparently threw a newspaper at him, he responded by slapping her around the face with three right-left blows.
A journalist at Antenna told the AFP news agency that colleagues were unable to stop Ilias Kasidiaris from leaving the building.
Golden Dawn has risen in profile after it won just under 7% of votes, or 21 seats, in parliamentary elections on 6 May.
The party’s staunch anti-immigration policy has led to accusations of racism and instigating violent attacks against immigrants.
Golden Dawn’s leader, Nikos Michaloliakos, has also denied the existence of gas chambers at Auschwitz and questioned the Holocaust, but he rejects the label neo-Nazi.
Greece’s political system has been thrown into disarray as the results of last month’s elections failed to give any party enough seats in parliament to form a coalition.
Another vote is due to be held on June 17 to try and end a political impasse that eurozone leaders say is harming Greece’s ability to tackle its economic crisis.
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