Dr Gietz is in New Zealand to oppose plans to introduce plain packaging.
He said Imperial Tobacco would leave open the possibility of a lawsuit against the New Zealand government if plain packaging is introduced, as planned.
He said it was a last resort but the company "will defend the right to use our brands".
After a long debate, a frustrated Ms Fox eventually got up and walked off set, telling Dr Gietz: "I'm not going to listen to you. I think you should crawl back into the hole that is reserved for corporate executioners."
Dr Gietz didn't react or rise to Ms Fox's inflammatory comments.
As she made her departing remarks, The Nation host Lisa Owen pleaded for civility, reminding her that Dr Gietz was an invited guest.
The host thanked both guests for joining the show and Dr Gietz replied: "Thank you for having me anyway".