“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.
“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 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”.
“Somebody who understands that the issues of our nation are not black or white. It cannot be boiled down to 140 characters,” she said, in a reference to Mr Trump’s enthusiasm for using Twitter.
“You can’t have thin skin or a tendency to lash out. You need to be steady and measured and well-informed.”