Nylon-6 nanofibrous membranes (NFM) prepared by electrospinning have been used as solid state support for the immobilization of the yeast Saccharomyces cerevisiae and then applied for the fermentation of grape juice. The membranes were characterized by scanning electron microscopy. The resulting metabolic activity was characterized by microcalorimetry. Sugar and ethanol changes during fermentation were monitored by HPLC. The results showed that the fermentation performance of immobilized yeasts on NFM is equal or even superior to the traditional fermentation process with yeasts freely dispersed in the medium. From calorimetry, free and immobilized yeasts showed the same enthalpy value in model solution, regardless to the amount of yeast loaded (52.2 ± 5.9 kJ mol−1 of glucose). Instead, immobilization of yeasts resulted in shorter lag time. Moreover, the maximum growth rate of immobilized yeasts was the same as with free yeasts in model solutions. However, the growth rate of immobilized yeasts was even higher, when performed in grape juice. In addition, the immobilization of yeasts on NFM exhibits the evident possibility of multiple reuse. Three consecutive fermentations were performed without significant loss of the overall performance. These findings support the development of nanostructured solid support for biocatalytic processes like fermentation of alcoholic beverages.