Pictures from the airport show the Boeing 737-400, operated by BA's partner Comair, tilting precariously on the runway on Monday.
On landing 94 passengers and six crew were evacuated on the tarmac without injury just after midday local time.
Comair is a regional airline which connects British Airways' long-haul routes from the UK to provincial airports across southern Africa.
It operates what is known as a 'codeshare' agreement whereby flight numbers and aircraft livery reflect BA's brand.
Comair said: "British Airways' (operated by Comair) BA6234 a 10:35 departure from Port Elizabeth, with 6 Crew and 94 Passengers on board, was involved in an incident on landing at OR Tambo International Airport just after 12:00 pm today.
"We can confirm that all passengers and crew safely disembarked with no reported injuries. Passengers have been taken to the terminal building where staff are on hand.
"Comair and the relevant authorities will be conducting the necessary investigation over the coming days and weeks. As soon we have more information on hand we will be releasing it to the media."
Passengers reported being asked to wait by crew members, despite flames being visible from inside the cabin. Minor injuries were reported during that flight's evacuation.