The adult film actress, whose real name is Stephanie Clifford, was performing on Wednesday night at Sirens club, in the city of Columbus.
An Ohio strip club law prohibits patrons from touching a nude or seminude dancer unless the patron is a member of the dancer's immediate family.
The patron is not believed to have been detained.
Michael Avenatti said in a tweet the charge was "politically motivated". "She was arrested for allegedly allowing a customer to touch her while on stage in a non sexual manner!"
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.
Since gaining nationwide prominence for her accusation against President Trump - and the $130,000 payment she received to originally keep quiet - Ms. Clifford has drawn crowds at strip clubs across the country, including in Greenville, S.C., Salem, Ore., and Des Moines, Iowa. "We will vehemently contest all charges".
A spokesperson for the Franklin County Sheriff's Department told CBS as of early Thursday morning, Daniels was not being held there.
Dailymail.com reached out to Sirens who refused to comment.
Trump forcefully denied the affair.
Daniels is suing the president and his former longtime personal lawyer and fixer Michael Cohen, and trying to invalidate a nondisclosure agreement she signed days before the 2016 presidential election.