In this study, the use of composite track-etched membranes (TeMs) based on polyethylene terephthalate (PET) and electrolessly deposited silver microtubes (MTs) for the decomposition of toxic phenothiazine cationic dye, methylene blue (MB), under visible light was investigated. The structure and composition of the composite membranes were elucidated by scanning electron microscopy, energy dispersive spectroscopy, and X-ray diffraction technique. Under visible light irradiation, composite membrane with embedded silver MTs (Ag/PET) displayed high photocatalytic efficiency. The effects of various parameters such as initial dye concentration, temperature, and sample exposure time on the photocatalytic degradation process were studied. The decomposition reaction of MB was found to follow the Langmuir–Hinshelwood mechanism and a pseudo-first-order kinetic model. The degradation kinetics of MB accelerated with increasing temperature and activation energy, Ea, was calculated to be 20.6 kJ/mol. The reusability of the catalyst was also investigated for 11 consecutive runs without any activation and regeneration procedures. The Ag/PET composite performed at high degradation efficiency of over 68% after 11 consecutive uses.