"I'm not going to sit here with no medical degree, listening to you with no medical degree, with an American flag behind you, smoking a cigar, acting like we know what's up better than the CDC [Centers for Disease Control and Prevention].
"All I do is I watch the news once every two weeks. I'm like 'Mask or no mask? Still mask? Alright, masks.' That's all I give a f**k about."
"But even they say you shouldn't wear a mask, unless you're treating a coronavirus patient," Rogan responded.
The World Health Organisation, in its latest advice however, says masks are part of a comprehensive package of the prevention and control measures that can limit the spread of Covid-19.
Burr jokingly took aim at Rogan's suggestion that masks are not manly.
"I just love how wearing a mask became like this f**king soft thing that you were doing — just being courteous," Burr said.
"Yeah, it's for b**ches," Rogan said, making a mocking cough.
"Oh god, you're so tough, with your f**king open nose and throat," Burr said.
Rogan laughed loudly at the exchange and toked on his cigar.
Some on social media have not seen the funny side, as you might expect.
Editor-at-large at The Daily Beast, Molly Jong-Fast, suggested Rogan's comments will cost lives if people don't follow the health advice.
"You know people are going to die because Joe Rogan and Donald Trump think masks are stupid," she said.
Here are some of the other responses to Rogan's comments and the social media attempt to "cancel" him.
• Covid19.govt.nz: The Government's official Covid-19 advisory website