She reportedly lured away from her friends by a group of men and it suspected she was gangraped, but police said Thursday they were still investigating.
The case has shocked the nation where tales of sexual violence are commonplace.
"The whole nation is outraged at this extreme violation and destruction of a young human life," President Jacob Zuma said in a statement Thursday.
"This act is shocking, cruel and most inhumane. It has no place in our country," he said.
"We must never allow ourselves to get used to these acts of base criminality to our women and children."
Official statistics show that around 65,000 sexual offences were committed in South Africa last year alone.
But police estimate that only one in 36 rape cases get reported.
The Cape Argus newspaper cited a witness saying that the teenager's body was cut open from her stomach through to her genital area, and exposed her internal organs.
Two suspects have been arrested and one of them appeared in court this week on murder and rape charges.
Studies have found that more than one quarter of South African men admitted to raping a woman or girl.
Government spokeswoman Pumza Williams said the "frequent occurrence of these brutal acts is unacceptable and will not be tolerated. This has to stop."
An "appalled and disgusted" Congress of South African Trade unions (COSATU), the main labour movement, has called for protests against rape following the incident.
"When a very similar incident occurred in India recently, there was a massive outbreak of protest and mass demonstrations in the streets," COSATU spokesman Patrick Craven said Wednesday, referring to the December gang rape of a student on a bus in New Delhi that shocked the world.
"We must show the world that South Africans are no less angry at such crimes and make an equally loud statement of disgust, and protest in the streets," he said.