Anthony Gardner said the former Ukip leader had given the President-elect a false impression that more countries might follow Britain out of the bloc by inflating the level of euroscepticism in Europe.
He added that it would be "lunacy" to follow Ukip's lead in supporting the "fragmentation of Europe" and urged Mr Trump not to treat the EU as "dysfunctional".
That approach would be "fundamentally flawed", he said.
He said: "For us to be the cheerleaders of Brexit and to be encouraging Brexit Mark 2, Mark 3, is the height of folly.”
Describing calls to EU institutions from Mr Trump's aides in recent weeks, Gardner said: "That was the one question that was asked - basically, 'What's the next country to leave?'. Which is kind of suggesting that the place is about to fall apart.
"It's just reflective of the general perception, a misperception, a perception that Nigel Farage is presumably disseminating in Washington and it's a caricature."
The ambassador said Mr Farage, who had written to him recently requesting a meeting, had misled Trump's transition team on the state of the EU.
"We should not depart from 50 years of foreign policy with regard to the EU," he said. "We should not become the cheerleaders for Brexit, particularly if Brexit appears more likely to be a hard, disorderly unmanaged Brexit."
He added: "A hard Brexit or a fragmentation of the European market would be very bad news for American business."
Mr Gardner also urged Europeans and the incoming US administration not to break ranks on sanctions against Russia over Ukraine.
American diplomats should speak frankly to the new leadership, even if that carried risks to their careers, he said.
Additional reporting by Reuters
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