Celebrity news website TMZ said this followed a physical confrontation between the lawyer and a woman.
He denied the claim, and was later released on a $50,000 (£38,500) bail.
The lawyer represents Ms Daniels, who alleges she and President Trump had a brief relationship - a claim he denies.
Ms Daniels has sought to free herself from a non-disclosure agreement she signed before the 2016 election.
A frequent guest on TV talk shows and news programmes, Mr Avenatti has emerged as a fierce critic of President Trump, the BBC's David Willis in Los Angeles says.
At one point Mr Avenatti was publicly contemplating running for president himself in 2020, our correspondent adds.
BBC
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