Sir David, 92, was on the show to urge people to take part in the Big Butterfly Count to assess the health of the environment.
But when Ms Munchetty, 43, tried to ask him about his conversations with the monarch while making the recent documentary The Queen’s Green Planet, the genial naturalist became irritated.
She began by asking Sir David what the Queen’s views were on plastic in the world’s seas, which he highlighted in his BBC documentary series Blue Planet II.
She told him: “You recently had a discussion with the Queen and we’re very keen to know if you discussed plastics with her.” Sir David replied: “No, we did not.”
She pressed on, saying: “Prince Charles, her son, has been a great advocate of helping the environment. It’s an issue that does seem to be held closely to the Royal Family’s heart.”
“That’s as maybe, yes,” said Sir David.
Sensing a chill, Ms Munchetty said: “I understand your reluctance to talk about that conversation but perhaps you’d be keen to talk about RRS Sir David Attenborough” – referring to a polar research ship Sir David recently launched on Merseyside.
He replied: “I wanted to talk about the Big Butterfly Count, that’s why you invited me here.”
After two more terse replies, Ms Munchetty returned to butterflies, asking why they were so colourful.
Sir David laughed before replying: “Butterflies are butterflies. We all know what butterflies are and they have different colours because butterflies have eyes and they can recognise prospective mates.”
The brusque encounter was soon the subject of social media comments.
One said: “Don’t think I’ve seen a much more awkward interview in a while than the one with David Attenborough on BBC Breakfast this morning.”
Another remarked: “Had to turn off BBC Breakfast when the David Attenborough/BBC Naga interview got deadly awkward. Gave me butterflies.”