News24 understands that the child was born at the Busamed Hillcrest Private Hospital last Thursday - Zuma's birthday.
Zuma is a polygamist who has fathered 22 known children from at least 11 women.
Three independent sources confirmed to News24 that Zuma came to visit his baby under strict security on Thursday night. "They had to clear the maternity ward for other patients. Hospital staff made it clear that this was strictly confidential," a source with direct knowledge of the birth told News24.
Ray Zuma, who is related to the former president, confirmed to News24 that Zuma was going to wed a woman named Nonkanyiso Chonco.
When asked if Chonco was the same woman who had given birth to a baby earlier this month, Ray Zuma responded by saying: "So?"
"I can't see why you are interested. When he was still the president, you [the media] were terrorising him, and now you are all of a sudden interested in him."
When asked about the details of the wedding, he said he was not privy to the details.
"No date has been set yet. Both families must come together to decide on the date. We are still in the pre-nuptial phases of the process."
Zuma's son Edward told News24, when asked about the baby: "We are not going to respond, or entertain any of that nonsense".
When News24 visited the hospital earlier in the week, an employee confirmed that Zuma had visited the facility.
"Yes he was here last week. I saw him with his security. I do not know why he came through."
But other sources confirmed the baby was Zuma's. Hospital staff were briefed to keep it a closely guarded secret and only told "this is JZ's child" and a "VIP delivery".
Hillcrest Private Hospital management declined to comment saying they would not divulge details of any patient.