The neo-Nazi activist had first thrown a glass of water at a lawmaker from the radical left Syriza party who was also participating in the debate.
When Kanelli, who had been sitting next to him got up to protest, he turned towards her, slapped her twice and then threw a punch before leaving the studio.
During the hearing, the prosecutor said that it was not appropriate for a man to beat a woman, but Kasidiaris refused to apologise for his actions unless his victim did the same.
Despite the outrage that the incident provoked, the party entered parliament for the first time in 2012 winning 18 of 300 seats.
The leadership of Golden Dawn is facing trial on charges including murder.