Her voice quivered as she recalled a meeting with young women at the White House on Tuesday.
"I told them they deserve to be treated with dignity and respect," Obama said. "I wanted them to understand that the measure of any society is how it treats women and girls."
Obama said the comments made by Trump in the video, which was recorded in 2005, had left her "shaken."
"I can't stop thinking about this," she said. "It has shaken me to my core in a way I could not have predicted."
She added: "I know this is a campaign but this isn't about politics. It's about basic human decency."
In the 2005 video, Trump can be heard describing in graphic terms how he uses his star power to force himself upon women. Since the footage was published last week by The Washington Post, several women have come forward to say that Trump had touched them inappropriately. Trump has denied those allegations, and has dismissed the remarks made in the video as "locker room talk."
At the rally on Thursday, Obama rejected that explanation.
"This was not just a lewd conversation," she said. "This wasn't just locker room banter. This was a powerful individual speaking freely and openly about sexually predatory behavior, and actually bragging about kissing and groping women, using language so obscene that many of us were worried about our children hearing it when we turned on the TV."
Referring to the spate of allegations levied against Trump, Obama said "it now seems very clear that this wasn't an isolated incident."
The speech was an uncharacteristically direct attack from the first lady, who said she eschewed her "normal campaign speech" because it would have been "dishonest and disingenuous to me to just move on to the next thing like this was all just a bad dream."
"This is not something that we can ignore," Obama said. "It's not something that we can just sweep under the rug as just another disturbing footnote in a sad election season."
Obama also cautioned against a "protest vote" and urged the supporters gathered to do "everything possible to elect Hillary Clinton."
"If you vote for someone other than Hillary ... you are helping to elect her opponent," Obama said.
"We need to recover from our shock and our depression," she added, referring to the sordid campaign developments, "and we need to do what women have always done in this country: we need to roll up our sleeves and get to work."
Clinton praised the first lady's support during a campaign event in San Francisco.
"If you haven't seen it, I hope you will see Michelle Obama's speech today in New Hampshire," Clinton said. "And once again, she gave a compelling and strong case about the stakes in the election, but about who we are as Americans. And we cannot let this pessimism, this dark and divisive and dangerous vision in America take hold in anybody's heart. We have to keep lifting up this campaign."