Dye wastewater is becoming one of the most significant sources of water pollution, and its impact on human survival is immeasurable. In this study, we successfully synthesized a nanofiber membrane with environmentally friendly and efficient properties using electrospinning of a mixture of sodium alginate (SA) and copper oxide (CuO) nanoparticles, aimed at effective dye removal. The adsorption performance of the SA/CuO nanofiber membrane was evaluated using the cationic dye methylene blue (MB). The maximum adsorption capacity of the nanofiber membrane was increased significantly with the addition of CuO nanoparticles, reaching a maximum value of 1633.4 mg g−1, almost twice as much as that of pure SA membrane. The adsorption kinetics follows the pseudo‐second‐order model, where chemisorption acts as the rate‐limiting step. The adsorption isotherm data indicate that the adsorption is monolayer. The nanofibrous membranes showed better dye removal under an alkaline environment. After four cycles of adsorption/desorption, the MB removal efficiency remained at 70.1% of the original adsorption capacity. The addition of CuO nanoparticles facilitated the adsorption of MB dyes, while the form of the nanofibrous membrane is easily recoverable and reusable. Therefore, the as‐prepared SA/CuO nanofibrous composite membrane is a potentially favorable adsorbent material for wastewater treatment applications.