A second person was seriously injured in the attack near Mopani Camp on Thursday (30 March) afternoon.
The victims were both wildlife park employees, it has been reported. Paramedics responded to reports of an animal attack and arrived at the scene, accompanied by rangers with rifles.
Jaco Gericke, of emergency services Maponya 911, told local newspaper Lowvelder the first victim suffered fatal injuries.
"The elephant tusk entered her lower back and exited her chest. She also had a severe open fracture to her left knee," he added.
The elephant is believed to have disappeared into the bush after the incident.
"I don't know if he was part of a herd," Gericke told Sky News. "The elephant was already gone when we arrived."
Officials are investigating the woman's death. The second victim suffered a broken femur, CBS news reports.
Kruger National Park is one of South Africa's best-known wildlife parks. There have been previous incidents at the wildlife reserve in which elephants have charged at cars which came too close to the herd.
In December 2013, one elephant charged a car, stabbing British woman Sarah Brooks in the thigh with its tusks.
Comment: Other attacks by African elephants over the past year include the following: Safari leader killed by elephant in Malawi
Elephant kills tourist in Kenya; 3rd attack in a month
Tourist trampled to death by elephant after provoking it by moving too near to takes pictures in Kenya
Elephant kills farmer in southern Tanzania; second death in 2 days
Selfie opportunity becomes fatal as elephant tramples man in Zimbabwe