Machado, who received the award for her efforts to promote democracy in Venezuela, had publicly stated her intention to share it with Trump, who has long expressed a desire for the prize.
The meeting took place less than two weeks after US military forces captured Nicolas Maduro, with Vice President Delcy Rodriguez now serving as interim president, whom Trump is engaging with.
While Trump acknowledged it would be an honour to receive the prize, he has previously suggested Machado lacks the necessary support to win a Venezuelan election.