The sleeve has a cloth tube comprising thermoplastic fibers and presenting a weld line (4) connecting two longitudinal edges and extending parallel to a median bend line of the tube. A lining (6) fixed on an upper outer side (2a) of the cloth tube partially covers the weld line. The weld line is formed using an ultrasound weld or thermo-welding machine producing a localized heating driving a fusion of cloth. An independent claim is also included for a method of fabricating a protection sleeve.