The former First Lady argued the President wants Americans “tuning out altogether” from the contest. She suggested his bombastic style during Tuesday’s presidential debate was designed to have this effect.
During the highly charged debate in Cleveland, Ohio, Mr Trump repeatedly interrupted Mr Biden and insulted his son.
The Democratic nominee in return told Mr Trump to “shut up” and called him a “clown”.
Posting on Instagram Ms Obama said: “If you were turned off by the President’s behaviour last night, I feel you. Believe me, I do.
“But we can’t let him win by tuning out altogether. That’s what he wants.
“So turn those feelings into action—turn them into votes for my friend, Joe Biden.
“It’s the only way we can get out of this chaos and restore some stability to this country.”
During Tuesday’s debate Mr Trump and Mr Biden clashed over the coronavirus, economy and law and order amongst other issues.
The two men had a particularly bitter exchange on the Supreme Court, where the president is attempting to appoint a replacement to Justice Ruth Bader Ginsburg who died earlier this month.
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At the end of the Supreme Court discussion Mr Biden sarcastically commented: “That was really a productive segment, wasn’t it?”
Referring to Mr Trump he added: “Keep yappin’, man.”
In her Instagram post Ms Obama urged American’s to contact friends and family and encourage them to vote.
She wrote: “You can start by reaching out to everyone you know. Make sure they’re registered.
“Make sure they know how and when they’re going to vote.
“And then follow up with them, every day, to make sure they cast their ballot.
“Because in this election, we’ve got to vote for Joe in numbers that cannot be denied.”
Mr Trump has repeatedly alleged, without providing evidence, that the election is being rigged via postal ballots.
As a result he has refused to guarantee he will accept the result.
Mr Biden is the current favourite to win November’s crunch election.