The wound dressings fabricated by polymers and oregano essential oil (OEO) can be very effective as a hydrogel. The current study has been focused on fabricating the hydrogel membranes of oregano oil encapsulated as an antibacterial agent into sodium alginate (SA) solution by solvent casting method and then evaluated the antibacterial, antioxidant activity, and physicochemical performance of SA/OEO-based polymeric membranes. The polymeric interactions, surface morphology, water absorption capability, thermal stability, and encapsulation efficiency were investigated by FT-IR, SEM, swelling ratio, DSC, and encapsulation efficiency. The percentage encapsulation efficiency of essential oil was 40.5%. FTIR validated the presence of molecular interaction between individual components. SEM images showed a rough and porous appearance for hydrogel membranes. Moreover, DSC showed that the fabricated membranes were thermally stable. The inclusion of more content OEO decreased swelling ratios. The antioxidant test was carried out by DPPH assay and antibacterial test through disc diffusion method against microbes. The results revealed that membranes containing the highest content of OEO had more excellent antioxidant and antibacterial efficacy. Therefore, the polymeric membranes of sodium alginate loaded with oregano essential oil can be employed as an effective wound-healing candidate.