Lilly Littlewood, 26, was taking a taxi to the Lima airport with her boyfriend Thursday when the taxi driver pulled a gun on the couple, Radio Programa del Peru reported.
Littlewood was shot in the stomach as she and her boyfriend tried to get out of the car.
The driver was later captured and some of the couple's possessions were recovered.
Littlewood's father traveled to Lima to be with her and said she has been moved out of the hospital's intensive care unit and is making good progress.
"She has undergone minor surgery to seal up the wound entry point; she has some internal damage but fortunately it missed 99 per cent of vital parts," he said.