Grammer was asked about his former wife, Camille, when he appeared on the Channel 7 breakfast show Sunrise earlier today. A clip from her US show, The Real Housewives Of Beverly Hills, was also shown.
The couple divorced acrimoniously in February.
The former Cheers star, who married Englishwoman Kayte Walsh – his fourth wife – days after the divorce was finalised, told presenters David Koch and Natalie Barr that he wanted to remain silent about his past relationship, preferring to “let his attackers fall”.
According to Aussie newspaper the Herald Sun, Grammer called the show’s producer, Mark Beirne, immediately after going off air.
The newspaper reports that Grammer was hurling profanities and “abusing” Beirne, saying: “You are a vile person… a sick dog… Your life must be tragic… I feel sorry for you”.
A source at Channel 7 also said Grammer would not be invited back onto any of its shows.
The five-time Emmy Award winner has declined to comment on the alleged incident.
The star is Down Under with his wife to host the Australian Commercial Radio Awards on the Gold Coast.
It is his first-ever trip to Australia.