The growing consumer demand for preservative-free food products has intensified research into antimicrobial biopolymers for food packaging. This study explores the antimicrobial potential of chitosan by developing a novel biopolymer through blending chitosan and whey protein in varying ratios (1:1, 1:2, 1:3) and incorporating essential oils to enhance antimicrobial efficacy. Mint and ginger essential oils were added at concentrations of 0.5%, 1%, 1.5%, and 2%, with initial screenings identifying the optimal composition as a 1:1 chitosan–whey protein matrix supplemented with 1% mint essential oil. The optimized biopolymer exhibited broad-spectrum antibacterial activity against a Gram-positive (Staphylococcus aureus) and a Gram-negative bacteria (Salmonella enterica Serovar Typhimurium), as well as a yeast (Saccharomyces cerevisiae). Notably, the presence of essential oils significantly enhanced the polymer’s antimicrobial properties, with superior efficacy observed in the essential oils compared to the polymer alone. Structural and physicochemical analyses demonstrated that the addition of mint essential oil improved the polymer’s surface uniformity, elasticity, and viscosity. Fourier-transform infrared (FT-IR) spectroscopy confirmed that the functional groups of the biopolymer remained largely unaltered upon mint oil incorporation. Mechanical testing revealed an increase in tensile modulus and a decrease in cutting modulus, alongside a minor reduction (2.35%) in melting point. Additionally, both the untreated and mint-enriched biopolymers exhibited decreased brightness and a slight tendency toward yellowing. These findings underscore the potential of chitosan–whey protein-based biopolymers, reinforced with essential oils, as sustainable and effective antimicrobial packaging materials for food preservation.