The pair were introduced after Prince Charles delivered a speech at the event in Switzerland, where sustainability is the main theme.
A "paradigm shift" is needed in the way the world deals with climate change, he said.
He outlined an initiative to encourage "rapid" decarbonisation and a shift towards sustainable markets.
Clarence House tweeted photos of his meeting with Miss Thunberg, who addressed delegates at the event on Tuesday.
Speaking shortly after US President Donald Trump, she strongly criticised politicians and business leaders for what she said were continuous "empty words and promises".
Prince Charles, the heir to throne, travelled around 80 miles to Davos from the Swiss city St Gallen in an electric Jaguar to deliver a keynote address to business and political leaders.
He said he is launching a "Sustainable Markets Initiative", which will bring together private and public sector leaders, heads of charities, and investors to work towards decarbonisation and a transition to sustainable markets.
He added that taxes could be used, as well as policies and regulations, to accelerate this shift.
His sons, the Duke of Cambridge and Duke of Sussex, and grandchildren have been in his mind throughout his environmental campaigning, he said.
He called for 2020 to be "the year that we put ourselves on the right track" and for the private sector to "lead the world out of the approaching catastrophe into which we have engineered ourselves".
"Do we want to go down in history as the people who did nothing to bring the world back from the brink, in trying to restore the balance, when we could have done? I don't want to," he said.
"Just think for a moment, what good is all the extra wealth in the world gained from business as usual if you can do nothing with it except watch it burn in catastrophic conditions."
Vote for the man who promises least; he'll be the least disappointing.