Prosecutor Hannes Cloete told journalists the State and defence counsel believed the evidence which was going to be presented was too sensitive.
He said the victim and the accused were minors and that the dignity of the families involved needed to be considered.
The State was about to lead evidence by Dr Tromp Els, a clinical forensic physician, in relation to the rape charge in the matter.
Northern Cape Judge President Frans Kgomo is hearing evidence in the trial of a 17-year-old youth accused of the murders of Northern Cape farmer Deon Steenkamp, 44, his wife Christelle, 43, and daughter Marthella, 14.
They were shot on their farm Naauwhoek on April 6, 2012.
The teenager also faces a charge of rape and defeating the ends of justice.
The evidence the State and defence did not want the media to report on was in relation to the alleged rape of the Steenkamp daughter.
The rape charge was added to the charge sheet in February by the State.
Els’s testimony was postponed to 2.15pm on Thursday for Kgomo to hear an official application by the State and the defence to exclude the media during Els’s evidence in chief.
At the start of the trial, Kgomo ruled that the media could be present at the trial, but that the youth could not be identified.
The high court is sitting as a children’s court in the matter.
The judge heard evidence from two Griekwastad farmers before the court was adjourned for the application.