Alice Walton, daughter of Walmart founder Sam Walton, was arrested for drink-driving on 7 October, the day of her 62nd birthday, in Fort Worth, Texas.
According to reports in the American press, Alice spent the night in jail and was released on a $1,000 (€725) bond.
Through her lawyer, the family business heiress apologised. “She accepts full responsibility for this unfortunate incident and deeply regrets it,” he said.
However Alice, who was once described by her father as “the most like me - a maverick - but even more volatile than I am", is not new to car accidents.
In 1998, she was convicted of driving under influence in Springdale, Arkansas. After hitting a gas meter and a telephone box, she reportedly refused to take a blood-alcohol test and asked a police officer if he knew who she was.
She was also involved in a car crash that resulted in the death of a 50-year-old pedestrian in 1989, but the police decided not to file any charges in that case, according to reports.