Marine chitinous byproducts possess significant applications in many fields. In this research, different kinds of fishery chitin-containing byproducts from shrimp (shrimp head powder (SHP) and demineralized shrimp shell powder), crab (demineralized crab shell powder), as well as squid (squid pen powder) were used to provide both carbon and nitrogen (C/N) nutrients for the production of an exochitinase via Streptomyces speibonae TKU048, a chitinolytic bacterium isolated from Taiwanese soils. S. speibonae TKU048 expressed the highest exochitinase productivity (45.668 U/mL) on 1.5% SHP-containing medium at 37 °C for 2 days. Molecular weight determination analysis basing on polyacrylamide gel electrophoresis revealed the mass of TKU048 exochitinase was approximately 21 kDa. The characterized exochitinase expressed some interesting properties, for example acidic pH optima (pH 3 and pH 5–7) and a higher temperature optimum (60 °C). Furthermore, the main hydrolysis mechanism of TKU048 exochitinase was N-acetyl-β-glucosaminidase-like activity; its most suitable substrate was β-chitin powder. The hydrolysis experiment revealed that TKU048 exochitinase was efficient in the cleavage of β-chitin powder, thereby releasing N-acetyl-d-glucosamine (GlcNAc, monomer unit of chitin structure) as the major product with 0.335 mg/mL of GlcNAc concentration and a yield of 73.64% after 96 h of incubation time. Thus, TKU048 exochitinase may have potential in GlcNAc production due to its N-acetyl-β-glucosaminidase-like activity.