The alleged incidents, which Green strenuously denies, are said to have occurred at the Canyon Ranch resort in Tucson, in 2016 and 2018.
Each count carries a potential sentence of up to 30 days in prison, a $500 (£400) fine and up to a year of probation, according to the Pima County Attorney’s office.
In an interview with the police, the accuser claims Green slapped her bottom.
A statement issued by Arcadia said: “Sir Philip 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 United States.”
The allegations come just a couple of months after Green took out an injunction, which barred newspapers from reporting on allegations of misconduct made against him by his staff. He again strongly denied these claims, and later withdrew the injunction.
A date for the first court hearing has been set for 19 June at Pima County Court.