The objective of our research was to evaluate the possible alteration of the organoleptic properties of eggs produced by hens (Lohmann Brown-Classic) fed with diets containing different doses of an industrial by-product enriched with organic zinc (Zincoppyeast, ZP): Control 0%, ZP 2.5%, and ZP 5.0%. Eggs were collected after 30 days (batch 1) and 60 days (batch 2) of feeding with the experimental diets and subjected to chemical, microbiological, human sensory, e-nose, and e-tongue analyses. There was no significant difference among the microbiological status of eggs of the three groups, but there were significant differences (p < 0.05) in the fat (9.5% vs. 9.3%) and protein contents (12.7% vs. 13.4%) of the Control and ZP 5.0% groups, respectively. Human sensory analysis showed no clear change in the organoleptic characteristics of the eggs. Using linear discriminant analysis (LDA), the e-tongue could recognize the three groups of eggs in batch 1 and batch 2 with 95.9% and 100% accuracy and had a prediction accuracy of 64.8% and 56.2%, respectively. When the eggs were incubating at 50 °C or 80 °C before the e-nose analysis, the groups of eggs could be recognized with 98.0% and 82.7% accuracy, and predicted with 68.5% and 62.2% accuracy, respectively, using principal component analysis-based discriminant analysis (PCA–DA). The aroma compounds and respective sensory descriptors showing changes among the different groups of eggs (batch, storage, and feeding) were identified based on the e-nose analysis. The sup-plementation of laying hens’ feed with the investigated industrial by-product can be applied without any substantial effect on egg quality, which can, however, be detected with advanced analytical methods.