Several hundred residents had gathered in the street ahead of Zuma's arrival, with many shouting "we want justice" and Zuma and his entourage were greeted by throngs of people outside the Pieters family home in Pluto Road.
Zuma was escorted into the home where he held a private meeting with the family, including Courtney's mother Jaunita, and family spokesperson Roegshanda Pascoe.
The meeting lasted for more than half an hour.
When Zuma emerged, he unveiled a plaque in memory of Courtney, which was fixed against the front wall of Pieters family home.
Addressing media afterwards, Zuma said: "In some cases, by people who are so intimate to us, something has gone wrong. I made a statement this morning and called upon South Africans to unite and fight against this. I think that enough is enough, we cannot allow this to happen."
Zuma then left the house and drove to nearby Epping where Courtney's body was discovered on Saturday, nine days after she had gone missing. A memorial site, with a cross and flowers, has been erected at the spot where her body was found.
Zuma spent several minutes pensively at the site.
A neighbour, Rachel Tait, said that Zuma's visit would not change anything, "he just visited since this became a big story on the news".
She added that the whole community was shocked because they all knew and respected the man accused of the killing.
Mortimer Saunders who lived with the Pieters family appeared in the Goodwood Magistrate's Court on Wednesday, facing charges of rape and murder related to the death of Courtney. "I don't know what went through his head because we knew him and he was a very nice guy hence this came as a shock to us," she said.
Another neighbour who did not wish to be named, said she hoped that "the government would help their community and make sure that people do not get away with crime".
"We need more lights in the streets so that people can see the spaces around them," the resident said.
Western Cape Community Safety MEC, Dan Plato, who also visited the home earlier, asked: "Rape a baby? She's not even a young girl, as far as I'm concerned, she's a baby. How is it that any adult man can get any right to rape a baby, kill a baby, hide the body?"