The officers spoke on condition of anonymity on Friday, since they were not authorised to release Hilton's name before she appears in court.
A spokesperson for police in Port Elizabeth, Brigadier Marinda Mills, declined to confirm the name, but said a high profile person was appearing in court on drug-related charges.
"This person is appearing in court right now. We cannot reveal information about her until she has appeared in court. I am here with the individual in court, we're waiting for the court to start," Mills told the Associated Press.
A local radio station in Johannesburg said Hilton was detained outside the Nelson Mandela Bay Stadium, following the quarter-final match between Brazil and Netherlands.
A police officer, who spoke on condition of anonymity, said Hilton was caught with an unspecified amount of marijuana.
"She was found in possession of some amount of dagga," the officer said, using the local name for marijuana.
"We don't know how much. It's a high profile person, only the top cops are dealing with it," he said.