The billionaire chairman of Arcadia group, the retail empire that includes Topshop, was charged on Friday with "knowingly touching another person with the intent to injure, insult or provoke" in 2016 and 2018, Deputy County Attorney Lauren E. Deakin for Pima County, Arizona, told CNN.
Each count of misdemeanour assault carries a potential sentence of up to 30 days in jail, a fine of not more than $500 and up to one year of probation.
The allegations of assault were made by Pilates instructor Katie Surridge who told police in Arizona that Green touched her inappropriately at the Canyon Ranch resort in Tucson.
In a statement given to CNN on behalf of Green, the businessman "strenuously denies these allegations and is disappointed that the charges have been filed in his absence and they are minor categories of misdemeanour in the US".
The statement also denied "any allegation of any sexual assault or misconduct made by the prosecution".
In a police interview, Surridge told Pima County Detective David Stivers that the "creepy old man" had "vigorously" slapped her bottom in January 2016. Surridge told resort staff, who said they spoke to Green and reassured her it wouldn't happen again.
However, in January 2018, Green took another class with Surridge and allegedly assaulted her again, according to the interview.
"Katie is aware charges were filed and trusts justice will take its course," Surridge attorney Peter Limperis told CNN on Friday night.
A spokesperson for Canyon Ranch told CNN they would not comment on the allegations but said they "do not condone or tolerate inappropriate behaviour towards our employees".
An arraignment date is set for June 19 in Tucson where Green will be represented by his lawyer.
( With inputs from IANS )