Ms Daniels was arrested for allegedly letting a customer touch her on stage “in a non sexual manner”, lawyer Michael Avenatti tweeted.
Ms Daniels became embroiled in a row with President Donald Trump after saying she slept with him in 2006, an allegation which he denies.
Her lawyer called the arrest “a setup” and “politically motivated”.
A Columbus police spokesperson has yet to respond to requests for confirmation about the arrest at the Sirens club in the north of the city.
Mr Avenatti tweeted that Ms Daniels, real name Stephanie Clifford, had been performing “the same act she has performed across the nation at nearly a hundred strip clubs”.
He said he expected her to be released on bail shortly and charged with a misdemeanour and vowed to “vehemently contest all charges”.
An Ohio law known as the Community Defense Act proscribes anyone touching a nude or semi-nude dancer, unless they are related.
Sirens tweeted last month to say Ms Daniels would make two “exclusive appearances” at the venue on the nights of 11 and 12 July.
A person who answered the phone at Sirens declined to comment.
Ms Daniels says she was paid $130,000 (£98,000) shortly before the 2016 presidential election to keep quiet about her alleged sexual encounter with Mr Trump.
She is trying to free herself from a non-disclosure agreement signed before the election, and suing over a “defamatory” tweet by the US president earlier this year. Mr Trump denies all allegations.