Plant biomass constitutes the main source of renewable carbon on the planet. Its valorization has traditionally been focused on the use of cellulose, although hemicellulose is the second most abundant group of polysaccharides on Earth. The main enzymes involved in plant biomass degradation are glycosyl hydrolases, and filamentous fungi are good producers of these enzymes. In this study, a new strain of Aspergillus niger was used for hemicellulase production under solid-state fermentation using wheat straw as single-carbon source. Physicochemical parameters for the production of an endoxylanase were optimized by using a One-Factor-at-a-Time (OFAT) approach and response surface methodology (RSM). Maximum xylanase yield after RSM optimization was increased 3-fold, and 1.41- fold purification was achieved after ultrafiltration and ion-exchange chromatography, with about 6.2% yield. The highest activity of the purified xylanase was observed at 50 °C and pH 6. The enzyme displayed high thermal and pH stability, with more than 90% residual activity between pH 3.0–9.0 and between 30–40 °C, after 24 h of incubation, with half-lives of 30 min at 50 and 60 °C. The enzyme was mostly active against wheat arabinoxylan, and its kinetic parameters were analyzed (Km = 26.06 mg·mL−1 and Vmax = 5.647 U·mg−1). Wheat straw xylan hydrolysis with the purified β-1,4 endoxylanase showed that it was able to release xylooligosaccharides, making it suitable for different applications in food technology.