For the first time, a biohybrid nanofibrous wound dressing is developed via green electrospinning of a blend solution of bovine serum albumin (BSA) (1 and 3 wt.%) and polycaprolactone (PCL). In such a system, the components are miscible and interact through hydrogen bonding between the carbonyl group of PCL and the amine group of BSA, as verified by ATR-FTIR. As a result, the biohybrid nanofibers show a superior elastic modulus and elongation (300% and 58%, respectively) compared with the neat PCL nanofibers. The included protein induces a hydrophilicity effect to the PCL nanofibers, notably at the higher BSA content (3 wt.%). In contrast to the neat nanofibers, the biohybrid ones are bioactive and encourage formation of biominerals (made of amorphous calcium carbonate) on the surface, after immersion in simulated body fluid (SBF). Based on the WST-8 cell viability tests, NIH3T3 fibroblast cells were seen to properly interact with the biohybrid mats and to proliferate in their proximity. SEM images show that the cells largely adhere onto such nanofibers even more than they do on the neat ones and adopt a flattened and stretched shape. In addition, the Live/Dead assay and Phalloidin/DAPI staining assay confirm large cell viability and normal cell morphology on the biohybrid nanofiber mats after 4 days incubation. Taken together, BSA/PCL nanofibers are able to offer optimum mechanical properties (elasticity) as well as mineralization which can potentially stimulate the wound healing process, and can be considered a suitable candidate for wound dressing applications.