Emergency services said the aircraft crashed on Tuesday after it took off on a test flight from a small airport.
Jurgen Kotze, chief operating officer for Emer-G-Med services, said the crash was near Wonderboom airport on the Moloto Road.
He said: "We suspect that the plane was on its way to the Wonderboom airport".
ER24 says paramedics are on scene, but adds, the exact number of injuries could still change.
"Some patients have been transferred already and some of them are still on scene".
Best Care ambulance services' Xander Loubser said reports indicated that the charter plane was carrying passengers on an global flight.
He said: "Initial reports show that approximately 20 people had sustained injuries ranging from minor to critical".
Meiring said there were two air ambulance helicopters on the scene.
The plane was marked Martin's Air Charter, but no information was immediately available about the air company.
The South African Civil Aviation Authority is on the scene investigating the cause of the crash.
"Paramedics are treating the patients and will thereafter transport them to a nearby hospital for further treatment".