The high porosity, interconnected pore structure, and high surface area-to-volume ratio make the hydrophilic nonwoven nanofiber membranes (NV-NF-Ms) promising nanostructured supports for enzyme immobilization in different biotechnological applications. In this work, NV-NF-Ms with excellent mechanical and chemical properties were designed and fabricated by electrospinning in one step without using additives or complicated crosslinking processes after electrospinning. To do so, two types of ultrahigh-molecular-weight linear copolymers with very different mechanical properties were used. Methyl methacrylate-co-hydroxyethyl methacrylate (p(MMA)-co-p(HEMA)) and methyl acrylate-co-hydroxyethyl acrylate (p(MA)-co-p(HEA)) were designed and synthesized by reverse atom transfer radical polymerization (reverse-ATRP) and copper-mediated living radical polymerization (Cu0-MC-LRP), respectively. The copolymers were characterized by nuclear magnetic resonance (1H-NMR) spectroscopy and by triple detection gel permeation chromatography (GPC). The polarity, topology, and molecular weight of the copolymers were perfectly adjusted. The polymeric blend formed by (MMA)1002-co-(HEMA)1002 (Mw = 230,855 ± 7418 Da; Mn = 115,748 ± 35,567 Da; PDI = 2.00) and (MA)11709-co-(HEA)7806 (Mw = 1.972 × 106 ± 33,729 Da; Mn = 1.395 × 106 ± 35,019 Da; PDI = 1.41) was used to manufacture (without additives or chemical crosslinking processes) hydroxylated nonwoven nanofiber membranes (NV-NF-Ms-OH; 300 nm in fiber diameter) with excellent mechanical and chemical properties. The morphology of NV-NF-Ms-OH was studied by scanning electron microscopy (SEM). The suitability for enzyme binding was proven by designing a palette of different surface functionalization to enable both reversible and irreversible enzyme immobilization. NV-NF-Ms-OH were successfully functionalized with vinyl sulfone (281 ± 20 μmol/g), carboxyl (560 ± 50 μmol/g), and amine groups (281 ± 20 μmol/g) and applied for the immobilization of two enzymes of biotechnological interest. Galactose oxidase was immobilized on vinyl sulfone-activated materials and carboxyl-activated materials, while laccase was immobilized onto amine-activated materials. These preliminary results are a promising basis for the application of nonwoven membranes in enzyme technology.