Consumers’ interest in a high-quality healthy diet is creating a growing trend in the food industry, focusing on the design and development of new products rich in bioactive compounds. This work involves the formulation of a vegetable sauce obtained from a mixture of pumpkin and pepper, the study of the evolution of bioactive compounds, quality and sensory parameters during storage at 4 and 25 °C, the influence of the packaging materials (PVC, PE/PA, and PS), and the migration degree. Antioxidant activity, polyphenols, carotenoids, and brown pigments contents were studied at 25 °C. Overall migration of the containers and the evolution of the physicochemical parameters and sensory attributes of the sauce were analyzed. All plastic materials showed an overall migration lower than the limit of EU and Mercosur Regulations. PVC better preserved polyphenols, antioxidant activity, and carotenoids until 50, 10, and 30 days, respectively, and lower development of brown pigments was observed. Higher storage temperatures favored undesirable changes in sensory attributes before 50 days of storage. PVC can be used to achieve greater conservation of the sensory attributes of sauce, regardless of the storage temperature. It could be considered the best material to preserve the bioactive properties and sensory attributes of the sauce until 30 days.