The 61-year-old responded by calling milkshake a "pathetic" thing for people to have thrown at their political opponents during May's European Union election campaigning.
She said "Certain unpleasant characters are being thrown to the fore and they're very, very easy to hate, and I'm kind of thinking, why bother with a milkshake when you could get some battery acid?". "That's just me, sorry". "It's purely a fantasy, but I think milkshakes are pathetic, I honestly do, sorry".
Mr Farage said it asked if in the current climate it was "inciting hate?"
UKIP EU parliamentary candidate Carl Benjamin, who has caused controversy with his rape "joke" about a female Labour MP, had a milkshake hurled at him while canvassing for support in Truro, Cornwall.
Brexit Party politician, Nigel Farage, has weighed into the debate, after previously fallen victim to having milkshake thrown over him. She has arguably done far worse by suggesting politicians should be doused with acid. "Shame on you, Jo Brand". Now, sadly, she is an idiot using her public presence to incite hatred and criminal acts'.
Coren Mitchell said the same show, the first of the series after a three-year hiatus, contained a joke about the Holocaust and her relatives and that "nobody" had complained about that.
But others disagreed with critics because the the comments were made on a comedic show that bills itself as a "discussion programme which challenges established ideas and questions received wisdom".
Some have been quick to defend Brand and her style of comedy, with fellow funny-man Lee Hurst sharing: "Jo Brand is a comedian". These people are truly scarred for life, so it takes a very unusual and sick mind to make jokes about corrosive liquid being thrown over people.The BBC were quick to sack Danny Baker for making an unacceptable joke following the birth of Harry and Meghan's baby.
The comedian went on to say she was joking and not a fan of the milkshake stunts. But will the BBC act in the same manner with Brand? If you're bothered by her joke, I wonder what you might think of Nigel Farage saying he'll pick up a rifle.