Naringin and limonin are the two main bitter compounds of citrus products such as grapefruit juice. The aim of this investigation was to evaluate the reduction in both bitter components simultaneously using a combined biochemical and physical approach. The proposed strategy was based on the use of heterofunctional supports with glyoxyl groups that allow for the covalent immobilization of naringinase, which hydrolyses naringin and alkyl groups that allow for the adsorption of limonin. The supports were butyl-glyoxyl agarose (BGA) and octyl-glyoxyl agarose (OGA), which were characterized in terms of aldehyde group quantification and FTIR analysis. The optimal pH and temperature of free and immobilized enzymes were assessed. The maximum enzyme loading capacity of supports was analyzed. Debittering of grapefruit juice was evaluated using soluble enzyme, enzyme-free supports, and immobilized catalysts. Enzyme immobilized in BGA reduced naringin and limonin concentrations by 54 and 100%, respectively, while the use of catalyst immobilized in OGA allowed a reduction of 74 and 76%, respectively, obtaining a final concentration of both bitter components under their detection threshold. The use of OGA biocatalyst presented better results than when soluble enzyme or enzyme-free support was utilized. Biocatalyst was successfully applied in juice debittering in five repeated batches.