“The hateful language… from public figures on TV does not represent the true spirit of this country,” she said, to loud cheers and applause.
“Don’t stoop to their level. Our motto is, when they go low, we go high.”
Earlier, Vermont Senator, Bernie Sanders urged Democrats to back Mrs Clinton.
She will accept the party’s presidential nomination on Thursday, when a roll call of how states’ delegates are voting is to be read out.
“While Donald Trump is busy insulting one group after another, Hillary Clinton understands that our diversity is one of our greatest strengths,” Mr Sanders said.
Some supporters of the senator, who had been Mrs Clinton’s rival in the Democratic primary, booed at mention of Mrs Clinton’s name; others wore duct tape with the word “silenced” over their mouths.
Mrs Obama’s speech was widely seen as an attack on Mr Trump, although she did not mention the Republican nominee by name.
She said she wanted her husband to be succeeded by “somebody who knows this job and takes it seriously” and that could only be Mrs Clinton.
Five times Michelle Obama referred to Donald Trump: “When someone is cruel or acts like a bully, you don’t stoop to their level. We urge them [our daughters] to ignore those who question their father’s citizenship or faith. Don’t let anyone ever tell you that this country isn’t great. Issues facing a president cannot be boiled down to 140 characters. Ideal president can’t have a thin skin or a tendency to lash out.”
Because of the Democrats’ candidate, she said, “my daughters and all our sons and daughters now take for granted that a woman can be president of the United States.”
In other remarks, she praised Mrs Clinton as a “true public servant” who had shown “devotion to our nation’s children” and “never buckles under pressure”.
After her speech, President Obama wrote on Twitter: “Incredible speech by an incredible woman. Couldn’t be more proud & our country has been blessed to have her as FLOTUS [first lady]. I love you, Michelle.”
Mr Trump, who has criticised his rivals, both Republican and Democrat, in sometimes colourful language on Twitter, said Mr Sanders had “sold out” to Mrs Clinton.
He also condemned other speakers at the Democratic convention, including senators Cory Booker and Elizabeth Warren, but made no mention of Mrs Obama.
In other key moments from the convention on Monday: Senator Warren attacked the business record of Mr Trump.
Comedian Sarah Silverman, who supported Mr Sanders, told his supporters to get behind Mrs Clinton
One of the loudest cheers went to Senator Booker when he told the crowd: “In America, love always trumps hate”