Staff members hurried into an enclosure at the park to fight off the lion and called an ambulance after the attack took place around 2:30 p.m. local time, or 8:30 a.m. ET, the spokesman, Scott Simpson told ABC News.
The woman, who was in the passenger seat of a car and has not been identified, died while emergency services were treating her, Simpson said, adding that the driver of the car, a tour operator, sustained injuries on his arm from fighting off the lion.
Witnesses quoted in South African media said they saw two people traveling in a car with their windows open. The lion is reported to have jumped at the woman through the open window and killed her.
A State Department official confirmed an American was killed at the park but declined further comment.
The lion responsible for the attack will not be euthanized, but could be moved to a private location, Simpson told ABC News.
Earlier this year, a lion attacked an Australian tourist in his car, though that tourist did not die from his injuries, Simpson added. He said the park has not had a fatal attack since the current management took over in 1999.
ABC News' Sifiso Khanyile in South Africa contributed to this report.