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.
Clinton told the BBC she will remain active in politics.
"I'm trying to make the case about what we need to do so that what happened in my election doesn't happen again," she said. "But I'll also be raising money and support for candidates and causes I believe in. And I'll be supporting the Democratic Party in the elections this year, next year and 2020."
She told the BBC she hadn't planned for the possibility that she would lose the 2016 election.
"I thought I was going to win, I thought I'd have the awesome responsibility and great honor of being the first woman president," she said.
"I had not worked on a concession speech, I had worked on a speech celebrating a victory. … And it all came crashing down," she said.
Describing the moment she realized she had lost the race as a "devastating personal loss," she said she felt "particularly terrible that someone I thought was not qualified or temperamentally suitable to be president was going to assume that office."