Fredie Blom's identity documents showed he was born in Eastern Cape province in May 1904, although that was never verified by Guinness World Records.
When he was a teenager, his entire family was wiped out by the 1918 Spanish flu pandemic. He went on to survive two world wars and apartheid.
Mr Blom told the BBC in 2018 that there was no special secret to his longevity.
"There's only one thing - it's the man above [God]. He's got all the power. I have nothing. I can drop over any time but He holds me," he said.
Mr Blom spent most of his life as a labourer - first on a farm and then in the construction industry - and only retired when he was in his 80s.
Although he gave up drinking many years ago, he was a regular smoker.
However, a coronavirus-related lockdown imposed by the South African government reportedly meant he was unable to buy tobacco to roll his own cigarettes on his 116th birthday.
Mr Blom's family said he died of natural causes in Cape Town on Saturday.
"Two weeks ago oupa [grandfather] was still chopping wood," family spokesman Andre Naidoo told AFP news agency. "He was a strong man, full of pride."
But within days Mr Blom shrank "from a big man to a small person", he added.
Mr Naidoo said the family did not believe his death was related to Covid-19.