The incident happened at around 9.30am local time on 30 March at the Kafue National Park in Zambia and the shocking video of the moment was captured and posted on social media.
The video showed the adult male elephant chasing the car which came to a halt as the animal closed in. The elephant then knocked the vehicle over as the guide screamed, "Hey, hey, hey!"
The woman has been identified as Gail Mattson by her family, according to ABC News. Safari operators, Wilderness Destinations, said the elephant "unexpectedly charged" at the vehicle that was on an excursion with six guests and a guide.
"An aggressive bull elephant charged the vehicle carrying six guests and a guide who were on a game drive from Lufupa Camp," the company said in a statement to ABC News.
"Our guides are all extremely well trained and experienced, but sadly in this instance the terrain and vegetation was such that the guide's route became blocked and he could not move the vehicle out of harm's way quickly enough," Wilderness CEO Keith Vincent said.
The group, which was staying at the Lufupa Camp inside the largest game reserve in Africa, had gone out for a photography tour at the time of the attack, the Telegraph reported.
The park dispatched a helicopter to the scene. The woman was airlifted and transferred to a hospital in South Africa after suffering unspecified injuries. She was pronounced dead at the hospital.
Four other people received treatment for minor injuries.
An investigation has been launched into the incident by local police and Zambia's Department of National Parks.
The local authorities and the US embassy in Lusaka are collaborating to repatriate the woman's body to her family. African elephants are among the largest land mammals on Earth.
Comment: Another attack reported in March this year: Angry elephant lifts safari truck into the air, 'traumatizes' tourists in South Africa