Speaking to BBC Radio 4's "Woman's Hour" program in comments aired on Tuesday, Clinton said: "No, I'm not going to run again."
She also said she would continue to oppose Trump. "I think I'm in a position where my voice will actually be magnified because I am not running (for office), and there's a very good basis, as we watch Trump's support shrink, that people will say, 'Well, what she said was right and now where do we go from here?'" she said.
Her comments came after Trump tweeted Monday that he hoped Clinton would run in 2020.
The secretary of State in then-President Barack Obama's administration and the first female presidential nominee of a major U.S. party lost to Trump in November's election. Clinton's campaign was dogged by accusations of impropriety regarding the use of a private email server while secretary of State.