Tannin acyl hydrolase, also known as tannase, is an enzyme with important applications in the food, feed, pharmaceutical, and chemical industries. However, despite a growing interest in the catalytic properties of tannase, its practical use is very limited owing to high production costs. Several studies have already demonstrated the advantages of solid-state fermentation (SSF) for the production of fungal tannase, yet the optimal conditions for enzyme production strongly depend on the microbial strain utilized. Therefore, the aim of this study was to improve the tannase production by a locally isolated A. niger strain in an SSF system. The SSF was carried out in packed-bed bioreactors using polyurethane foam as an inert support impregnated with defined culture media. The process parameters influencing the enzyme production were identified using a Plackett-Burman design, where the substrate concentration, initial pH, and incubation temperature were determined as the most significant. These parameters were then further optimized using a Box-Behnken design. The maximum tannase production was obtained with a high tannic acid concentration (50 g/l), relatively low incubation temperature ($30^{circ}C$), and unique low initial pH (4.0). The statistical strategy aided in increasing the enzyme activity nearly 1.97-fold, from 4,030 to 7,955 U/l. Consequently, these findings can lead to the development of a fermentation system that is able to produce large amounts of tannase in economical, compact, and scalable reactors.