Erasmus said he initially thought the cold sensation he felt through his shirt was his water bottle leaking.
"As I turned to my left and looked down, I could see the head of the snake receding back underneath my seat," Erasmus told NPR. "At which point there was a moment of stunned silence, to be brutally honest."
Erasmus said it took him a few moments to register that he had just seen a highly venomous cape cobra.
The pilot quickly made arrangements for an emergency landing at the closest airport, in Welkom, and informed his passengers of the slithering stowaway.
"You could hear a needle drop and I think everyone froze for a moment or two," he told the BBC.
Unlike the 2006 film, the plane landed with no one being bitten by the cobra. The passengers and crew members disembarked safely.
Erasmus said the snake was still curled up under his chair when he disembarked, but the reptile had disappeared by the time a professional snake catcher arrived on the scene.
Workers at Worcester flying club, where the plane had originally departed, revealed they had earlier seen a snake slithering under the aircraft, but it vanished before they could grab it.
Poppy Khosa, South Africa's civil aviation commissioner, hailed Erasmus as a hero.
"Oh my goodness this could have been disastrous. Great airmanship indeed, which saved all lives on board. Such an amazing story and great handling of the situation by the pilot. Bravo to great airmanship," Khoza told News24.