Mr Musk and Ms Bezuidenhout’s mother had two children together before divorcing after 18 years of marriage.
He told The Sunday Times that his stepdaughter had contacted him last year after splitting up with her boyfriend.
“We were lonely, lost people,” he said from his home in South Africa. “One thing led to another — you can call it God’s plan or nature’s plan.”
Two months later Ms Bezuidenhout told Mr Musk she was pregnant and a paternity test revealed he was the father.
The news of the baby reportedly caused a rift between Mr Musk and his other children.
His son, tech billionaire Elon Musk was allegedly “outraged” when he heard about the baby.
A relation to the family told the MailOnline: “The whole family was outraged when we found out. This is the reason why Elon is so angry with Errol. He is the only father she has ever known. And now he is the father of her child as well.”
The entrepreneur, who is in a relationship with actress Amber Heard, previously described his father as “evil” in an interview with Rolling Stone magazine.
He said his father had committed “almost every crime you can possibly think of” and done “almost every evil thing you could possibly think of”.
Errol Musk disputed his son’s portrayal of him but has admitted shooting dead three intruders in his home in South Africa, for which he pleaded self-defence to a manslaughter charge and was acquitted.
Mr Musk senior is a millionaire who made his fortune through engineering.
He told The Sunday Times that he thought his children were “spoilt.”
“They were spoilt, I suppose. Maybe that’s why Elon is acting like a spoilt child now,” he said.