The porn star's lawyer said the arrest "reeks of desperation", and said Daniels was performing the same routine she had done "at almost a hundred strip clubs" throughout the country.
The patron is not believed to have been detained.
Mr Avenatti wrote: "This was a setup & politically motivated". Officers knocked on the door of her tour bus after the performance and took her into custody in an arrest that Avenatti said left her "traumatized and rattled". In May, Trump said Daniels was paid to stop "false and extortionist accusations" she made about a sexual encounter with him.
She was set to perform at the club again Thursday night, but had to cancel her performance. "While the presence of Vice officers at this establishment is reasonable, the motivations behind the officers' actions will be reviewed internally", she said in a July 12 statement.
Daniels, real name Stephanie Clifford, is suing Trump and his former personal lawyer Michael Cohen to nullify a 2016 non-disclosure agreement preventing her from speaking out about an alleged affair she says she had with Trump in 2006. It reeks of desperation.
But cops said in the arrest report that it was Daniels who was "forcing the faces of patrons into her chest and using her bare breasts to smack the patrons" - and then did the same thing to both male and female cops. He vowed to fight the "bogus charges", even suggesting there are "higher priorities" at stake for the police.
A person who answered the phone at Sirens declined to comment.
Charles Murphy, a correctional service coordinator at the Franklin County Sheriffs' Office, confirmed Daniels was arrested by a Columbus police officer but said she hadn't been booked. Trump has denied it.
She is trying to free herself from a non-disclosure agreement signed before the election, and suing over a "defamatory" tweet by the USA president earlier this year.
However, the Republican president - who initially denied knowledge of the payment - subsequently conceded that Cohen was in fact reimbursed.