The incident happened during the recording of Africa 360, a current affairs show on the eNews Channel and on eNews Africa.
Visagie was being bombarded with questions by political commentator Lebohang Pheko.
The dramatic footage of the showdown was aired during eNews Prime Time at 19:00 on Wednesday night.
Visagie became visibly incensed with Pheko and decided to pull the plug about 30 minutes into the interview.
He stood up, ripped off his microphone and threw it aside and told Pheko: "Don't you dare interrupt me."
At this point, the host, Chris Maroleng, tried to intervene, but Visagie said, "don't touch me".
Maroleng responded with: "you won't dare touch me in my studio."
Security was brought on set and Visagie started to make his way to the exit.
But he then turned back, pointed at Pheko and said: "I'm not finished with you."
Group head of eNews Patrick Conroy said the interview was about the relationship between farm workers and their bosses.
This comes in the wake of the murder of AWB leader Eugene Terre'Blanche.
Pheko had asked Visagie: "Do you care about millions of South Africans? Do you care about farm workers who are still oppressed by farmers?
"Is it you (whites) versus us (blacks)?"
Visagie replied: "You don't understand our street names. You don't understand our culture."
'Right to leave'
Talking to The Witness after the incident, Conroy expressed disappointment at the event.
"Enews is disappointed in the behaviour of the AWB's secretary general.
"We understand that debates can get heated from time to time, and guests will interrupt one another, but this is not an excuse to lose one's tempter or threaten others.
"If Mr Visagie was unhappy with the interview he had every right to leave."
He commended the way Maroleng handled the situation.
"Chris Maroleng was calm and tried to defuse the situation and prevent it from escalating. eNews management is happy with the way he dealt with the situation.
"He continued to refer to the secretary general as 'Mr Visagie' and was polite but firm."
"Mr Visagie and his bodyguard promptly left the premises without further incident," he said.
Sources said Visagie had demanded his bodyguard be present during the interview.
As things became heated in the studio, a lean-looking youth with a smile on his face came on camera and stood beside Visagie.
'He called me names'
Pheko told The Witness after the interview that she was taken by surprise by Visagie's outburst.
"This was a discussion about race relationships, but Visagie became very irritated," said Pheko.
"He was even calling me names."
Pheko said that although she had predicted Visagie would be defensive during the interview, she did not expect such a dramatic reaction.
"He just exposed himself as a person who is not interested in this nation, and who is only interested in the Afrikaners," she said.
"This reminds us that our democracy is still fragile. There are still elements who are looking for any excuse to (destabilise) our nation," she said.
She said when Visagie stood up from his chair she was confused.
"It happened so fast that I did not get time to think. I kept hoping that his bodyguards were not carrying guns," Pheko said.
Beeld's Retha Grobbelaar reported that Visagie said on Wednesday that he felt "insulted and belittled" and thus decided to leave the studio.
"I reached a point where I decided I'm not going to carry on. My people, my volk and my history were constantly being belittled. They provoked me repeatedly," he said.
According to Visagie, he phoned Gwede Mantashe, secretary general of the ANC, after the incident.
"I told him these people are inciting racial conflict while he's trying to make peace between races. He said he will address the issue immediately."