Obama's comments came in an interview with Parade magazine, excerpts of which were published on its website.
Asked if she thinks the country will see a female president in her lifetime, the wife of President Barack Obama said: "Yes, I think the country is ready for it. It's just a question of who's the best person out there."
She declined to comment on the prospects for Clinton running to succeed Obama in 2016.
Hillary Clinton, a former US senator and secretary of state under Obama during his first term, has been vague on whether she will seek the nation's highest office.
She left her post as the top US diplomat in February and polls released with the Democratic nominating convention still three years off say she is ahead - both in the Democratic primaries and in the theoretical general election.
Of Clinton's prospects, Mrs Obama said, "She hasn't announced anything, so I'm certainly not going to get ahead of her."
She added that she herself will not run for president.
Obama also said she thinks her husband's time in office has helped ease racial prejudice in the United States.
"Children born in the last eight years will only know an African-American man being president of the United States. That changes the bar for all of our children, regardless of their race, their sexual orientation, their gender," Obama said.