The current study aimed at the valorization of bread waste in a fungal biorefinery for the recovery of protein hydrolysate for food applications and monofilaments for medical textile applications. Rhizopus delemar was cultivated on bread waste in a 1 m³airlift bioreactor to obtain fungal biomass. The protein hydrolysate was isolated as a soluble fraction after a mild enzymatic treatment of fungal biomass with a protease enzyme. The recovered protein hydrolysate was rich in eight essential amino acids and showed foaming and emulsion properties. The fungal microfibers rich in chitin and chitosan were recovered as an insoluble fraction of fungal biomass during the protease treatment process. A hydrogel of the fungal microfibers was wet-spun to monofilaments, which showed high elongation at break. In in vitro scratch assay, the monofilaments demonstrated significant improvements of the rate of cell migration and wound closure compared to viscose fibers (which are commonly used in wound healing dressings). Furthermore, fungal biomaterials in the form of microfibers, hydrogel, and monofilaments showed excellent biocompatibility against fibroblast cells and significantly enhanced cell growth at higher concentrations (above 500 μg/mL). This work suggests a sustainable approach to using abundant food wastes to create value-added products for food and medical textile applications.