Sir Philip Green "strenuously denies" four charges of misdemeanour assault brought against him in the US, his lawyer has told Sky News.
A pilates instructor, Katie Surridge, alleges the 67-year-old retail tycoon touched her inappropriately.
It is said to have happened during classes at the Canyon Ranch luxury resort in Tucson, Arizona, in 2016 and 2018.
Sir Philip is accused of knowingly touching another person with the intent to injure, insult, or provoke, Pima County Attorney's Office said.
Deputy county attorney Lauren Deakin said: "Philip Green has been formally charged with four misdemeanour assault counts.
"These are class three misdemeanours. Each count has a potential sentence of up to 30 days in the Pima County jail, a fine of not more than $500, and up to one year of probation."
Ms Deakin said an arraignment date had been set for 19 June.
More from UK
Sir Philip, who owns retail company the Arcadia Group, "strenuously denies" the allegations, his lawyer Ian Burton told Sky News.
Arcadia said in a statement that Sir Philip was "disappointed that the charges have been filed in his absence and they are minor categories of misdemeanour in the United States".
It continued: "Sir Philip is not personally required to attend before the court at the forthcoming hearing and will be represented by his lawyer.
"Contrary to previous suggestions in the media there is no allegation of any sexual assault or misconduct made by the prosecution."
A spokesperson for Canyon Ranch said the resort would "not comment on these allegations".
They added: "Canyon Ranch does not condone or tolerate inappropriate behaviour towards our employees.
"Canyon Ranch has strict policies and procedures that prohibit inappropriate behaviour, and takes prompt, remedial action with respect to inappropriate behaviour allegations."