β-Galactosidases are widely used for industrial applications. These enzymes could be used in reactions of lactose hydrolysis and transgalactosylation. The objective of this study was the production, purification, and characterization of an extracellular β-galactosidase from a filamentous fungus, Aspergillus niger. The enzyme production was optimized by a factorial design. Maximal β-galactosidase activity (24.64 U/mL) was found in the system containing 2% of a soybean residue (w/v) at initial pH 7.0, 28 °C, 120 rpm in 7 days. ANOVA of the optimization study indicated that the response data on temperature and pH were significant (p < 0.05). The regression equation indicated that the R2 is 0.973. Ultrafiltration at a 100 and 30 kDa cutoff followed by gel filtration and anion exchange chromatography were carried out to purify the fungal β-galactosidase. SDS-PAGE revealed a protein with molecular weight of approximately 76 kDa. The partially purified enzyme showed an optimum temperature of 50 °C and optimum pH of 5.0, being stable under these conditions for 15 h. The enzyme was exposed to conditions approaching gastric pH and in pepsin’s presence, 80% of activity was preserved after 2 h. These results reveal a A. niger β-galactosidase obtained from residue with favorable characteristics for food industries.