In recent years, consumers have shown considerable attention to functional foods that can provide various benefits. At the same time, the awareness of the problem of waste generation from the agri-food supply chains has increased; thus, scholars and practitioners are devoting great attention to sustainable food waste management. Within the wine processing, the production phase generates by-products such as marc, grape seeds, stems, and wine lees. In most cases, these by-products are treated as waste rather than as a resource, creating environmental, economic, and social impacts related to their disposal. By contrast, the reuse of oenological by-products in food production can have several health benefits, since they are rich in functional molecules such as fibres, polyphenols, and vitamin E, and can also trigger a circular economy model. The aim of this research is to investigate the acceptance of consumers towards bread enriched with oenological by-products through the application of k-means clustering, providing insights on the characterisation of groups of consumers based on their specific features and declared attitudes. The results showed three different consumers’ clusters, highlighting that the acceptance of this enriched bread is not influenced by the consumers’ socio-economic features, but it is related to consumers’ sensitivity. Therefore, target strategies should be put in place to inform consumers about the benefits associated with the consumption of bread enriched with oenological by-products.