The 94 passengers and six crew on board flight BA6234 disembarked safely.
The Boeing 737-400 plane - owned and operated by South African franchise Comair - had flown to OR Tambo International Airport from Port Elizabeth on Monday.
South African authorities are investigating what caused the incident.
Emergency services helped passengers and crew safely off the plane. No injuries have been reported.
Comair said in a statement that the plane experienced a landing gear problem shortly after touching down, at around midday local time (10:00 GMT).
"The aircraft was on the runway for a short period performing standard landing procedures when the crew noticed an unusual vibration which was followed shortly by the collapse of the left landing gear," the company said.
Passenger Warren Mann said: "When it came into land, it felt like the touchdown was a bit harder than normal - then it felt like a piece of something had fallen off.
"Oxygen masks came down and the plane was at an angle as we touched down.
"We could smell something burn and fire crews were soon at the plane to deal with the engine.
"Only afterwards did we find that the left landing gear had broken off."
Airports Company South Africa, which owns the airport, said the runway was temporarily closed, causing some delays.
Comair operates regional and local flights in South Africa. It flies as a British Airways franchise, with aircraft painted in BA livery.
Emergency crews were called to help a British Airways franchise flight after its landing gear collapsed soon after touching down in Johannesburg.