Photographs from the scene of the crash show the damaged aircraft in a field.
"Initial reports show that approximately 20 people had sustained injuries ranging from minor to critical".
The aircraft, a Convair 340 (ZS-BRV) was taking off from Wonderboom airport.
Police spokesman Isaac Mahamba told South African broadcaster eCNA: "There is smoke all over and paramedics are on the scene".
"We are unsure as yet of how the incident occurred".
The Aviodrome aerospace theme park near the central Dutch city of Lelystad said on its Facebook page that it was "hugely shocked" by the crash.
One person died in a plane crash in Wonderboom, Pretoria, July 10, 2018, emergency responders said.
A plane crashed in Pretoria, South Africa, on Tuesday afternoon.
It had been due to fly to Aviodrome via east Africa, through Egypt, Croatia, Austria to the Netherlands. "Paramedics are treating the patients and will thereafter transport them to a nearby hospital for further treatment". Martin's Air Charter is an affiliate of Air France-KLM.
The South African Civil Aviation Authority said a team of investigators had already been sent to the scene to investigate the cause of the accident.