"Paramedics found the bodies of three people lying inside the aircraft," ER24 medical service told News24 website.
The plane crashed into shacks in Benoni, about 40km (25 miles) east of the city.
Footage on social media show emergency services taking bodies away from the crash site.
The BBC's Pumza Fihlani in the city says incidents like this are not common in South Africa.
The country has a very good record of air safety, she adds.
A light aircraft has crashed in the South African city of Johannesburg, killing all three people on board, emergency officials have said.