Brider admitted he served six years in prison but no further context was given to the story.
Jeremy's mother, Donna Travers, said the show's producers should have ensured the full facts of the crime - including his seriously assaulting three other people on the same night - were fully disclosed to audiences.
She said representatives from the show had contacted her today to say the apology would take place.
The family had no idea Brider would appear on the show or discuss Jeremy's death, and Ms Traver's daughter and sister were both watching it when the segment came on.
She the issue was never whether or not Brider deserved a "second chance" after serving the sentence for his crime, but that incorrect and misleading information was broadcast about the case.
MediaWorks spokeswoman Rachel Lorimer said in a statement:
"MediaWorks wants to apologise again for any distress or hurt caused by the episode of The X Factor NZ that featured Shae Brider.
"We take the impact it has had on the victim's family very seriously, and have today been talking with Donna Travers both to apologise personally and to discuss with her the best way to add to yesterday's public apology.
"As a result of these conversations, we will be starting the Sunday and Monday night episodes of The X Factor NZ with an apology to Donna and her family.
"We hope this will go some way towards alleviating the hurt and distress the family have suffered as a consequence of Tuesday's episode."