Aguilera had already recorded the duet with the image of the deceased star.
Pat Houston, the executor of Whitney's estate, said the hologram in its present form is simply too low-tech for the family to allow it appear on a primetime broadcast, reported Entertainment Tonight.
"We are so appreciative of the opportunity for the Whitney Houston hologram to appear on NBC's 'The Voice' with a talent pairing as extraordinary as Christina Aguilera and Whitney Houston," Pat said.
She emphasised the decision to scrap the TV duet was purely based on the technology and had nothing to do with Aguilera.
"After closely viewing the performance, we decided the hologram was not ready to air. We have much respect and appreciation for Christina, and she was absolutely flawless."
Whitney's estate executors sealed a deal with Greek billionaire Alki David, the CEO of Hologram USA and FilmOn, last year to create a three-dimensional laser image of the Grammy-winner.