The South African Civil Aviation Authority said the crash happened at around 9am.
The accident was reported by the Aeronautical Rescue Co-ordination Centre.
The scene was a hive of activity with various responders present including medic teams, rescue teams, the South African Police Service and the Johannesburg Metro Police Department.
The aircraft had departed from Grand Central Airport in Gauteng on a training flight with the intention to land back at the same airport.
The aviation authority said a preliminary report would be issued in 30 days.
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