The 22-year-old victim, who has not been identified, was visiting a camp at the popular Dinokeng Game Reserve, near Pretoria, when she was attacked close to her vehicle.
According to a statement posted to Richardson's Instagram account
, the lioness was pursing an impala at the "big 5" reserve, which is also home to leopard, rhino, elephant and buffalo, when it encountered the woman and her friend.
The victim died at the scene, confirmed the paramedics
who responded to the incident.
Richardson's intimate relationship with lions and other wildlife has been documented in several books and documentaries, earning him fame across the world.
"Myself and an experienced colleague took three lions walking in the reserve, as we do on a weekly basis, as part of their exercise and stimulation regiment," said Richardson in his statement.
"We assessed the landscape for other big five animals and as per procedure sent out a notification that we were walking in the reserve."
"One of the lionesses charged off after an impala and must have run 2 to 2.5 kilometers (1.2 to 1.5 miles), where she encountered the 22-year-old outside the car."
"I am devastated and my heart goes out to this young woman's family," said Richardson.
The popular "free-roaming" reserve rotates lions through vast roaming enclosures, providing them with "the ability to live out full lives, in an open and natural environment," according to its website.
On social media, supporters of Richardson offered condolences to the victim while rallying to defend the sanctuary, which is located inside the larger reserve, for its conservation efforts.