She has filed two lawsuits against Trump, who denies he had an affair with her in 2006.
Daniels, whose real name is Stephanie Clifford, was arrested by Columbus Police.
Ohio's Community Defense Act prohibits touching a nude or semi-nude dancer in a club, besides members of the dancer's immediate family.
The law refers to someone "who regularly appears nude or seminude" at a club.
Booking photo of Stormy Daniels. "The officers also observed Ms. Clifford fondling the breasts of female patrons", Franklin County Municipal Court records show.
He added that Daniels meant to plead not guilty. She shoved each of their faces between her breasts, court documents said. According to police docs, Stormy put both hands on Officer Mary Praither's butt and breasts, and then put her breasts in the officer's face. Daniels, Miranda Panda of Marion, Ohio, and Brittany Walters of Pickerington, Ohio, were each charged in the undercover operation. Reached by The Washington Post early Thursday, a representative for Sirens strip club refused to comment.
"It reeks of desperation", Avenatti tweeted.
"We are highly confident that in the unlikely event that the district attorney proceeds with charges that she will be found not guilty", Avenatti told The Post. "There has to be higher priorities!" he continued.
Avenatti said Daniels was arrested while "performing the same act she has performed across the nation at almost a hundred strip clubs".
'This was a setup and politically motivated.
"We will vehemently contest all charges", he said.
However, police say they were there investigating complaints of alleged prostitution and drug activity.
In an official statement via Avenatti, Daniels announced that she is canceling her Thursday night performance. Trump has forcefully denied the affair.
Just days before the 2016 election, Mr Cohen paid Daniels $130,000 (£98,400) in exchange for her silence.
He initially said he used his own money to pay Daniels and was not reimbursed by the president. If a dancer violates it, management usually takes care of the matter, she said. After Stormy's performance, she and the other 2 were arrested at the same time.
"This was a complete set up", he said. "She was putting on a show".