The comedian and activist claimed in a blog, published on the the Huffington Post UK, that the Ukip leader had made the controversial remarks during a "practise question" before recording started for the BBC show.
"The practice question is a soft ball rhubarb toss about clumping kids or something," he wrote. "Farage says it's okay to hit children. "It's good for them to be afraid" he said. There is a lot of fear about in our country at the moment and he is certainly benefiting from it."
In response, Ukip told the Huffington Post UK that Farage had actually told the Question Time audience that "it is good that children fear the consequences of breaking rules set by their parents".
A Ukip spokesman added that Farage's remarks were "quite different" from saying that "kids should be fearful".
He claimed Brand had responded to Farage's remarks during the practise question by quipping: "Why stop at your own children?"
The early clash arose after an audience member is believed to have asked the panel why parents shouldn't be able to smack their own children.
Others also expressed doubt about Brand's accuracy in his account, with the Daily Mirror columnist Fleet Street Fox noting that the actor described the table panellists sat on as wooden, when it is clear perspex.
"I don't think he was paying the least bit of attention," she wrote.