The present research was carried out with the objectives of isolating fungal strains capable of exhibiting inulinase activity from a novel source, then optimizing solid state fermentation for the inulinase production and characterizing crude enzyme. Production of inulinase is first reported in this study with a novel substrate, banana plant shoot powder, using newly isolated fungal strain Nothophoma anigozanthi JAM through solid state fermentation. The fungal strain was isolated from the root soil of a white Jamun (Syzygium cumini) tree. Optimization of the solid state fermentation was carried out by central composite design for determining the interaction and impact of the influential process on inulinase production. A mathematical model was developed based on the statistical analysis and recommended optimal process conditions of 2 g of substrate, 5 mL of moistening media, 5 mL of inoculum volume, and 96 h of fermentation time for enhanced production (2.578 U/gds). Crude inulinase enzyme exhibited an 8.0-fold increase in activity after optimization, in comparison with the activity under unoptimized conditions. The optimum pH (5.0), temperature (60 °C) for the enzyme activity, and Km (0.205 mM) and Vmax (0.333 µM/min) were determined based on the biochemical and inulin hydrolytic properties of the crude inulinase enzyme. The production of inulinase was further validated by using TLC, osazone, and Seliwanoff tests. Hence, the inulinase enzyme produced by Nothophoma anigozanthi JAM can be successfully utilized for the production of edible sugar fructose from non-edible polysaccharide inulin, present in agricultural residues such as banana shoot by solid state fermentation.