The development of inorganic membranous catalysts with both large mesopores and superb flexibility is extremely favorable for the enhancement of their catalytic oxidation activity for the degradation of antibiotic pollutants in wastewater via sulfate radical-based advanced oxidation processes; however, there still exists a huge challenge for inorganic materials to simultaneously realize these two properties. Herein, metallic copper-doped carbon/silica nanofibrous membranes (Cu@C/SiO2 NFMs) with large mesopores, superb flexibility, and robust mechanical strength were fabricated through a sol-gel electrospinning and subsequent in situ carbonization reduction method. The synthesized Cu nanoparticles were homogeneously distributed throughout the mesoporous C/SiO2 nanofiber matrix, which enabled the resultant Cu@C/SiO2 NFMs to be applied as heterogeneous catalysts, and their catalytic performance was systematically assessed through activating persulfate for the elimination of tetracycline hydrochloride (TCH) in water. The fabricated Cu@C/SiO2 NFMs provided outstanding catalytic performance towards TCH with a high removal efficiency of 95% in 40 min and a rapid removal speed of 0.054 min-1. Moreover, the membranes could be facilely recycled through being directly separated from water without any post-processing. Such a facile strategy for preparing mesoporous and flexible metal-doped inorganic nanofibrous membranes may offer novel insights for designing new types of heterogeneous catalysts for antibiotic-containing wastewater treatment or other potential applications.