With the aid of experimental design, in this study, we have investigated the activity and stability of dextranase, an important extracellular inducible enzyme that specifically hydrolyzes the α-1,6 glycosidic linkages of dextran, leading to the formation of D-glucose and shorter oligosaccharides. The experimental design results showed the significant individual as well as interaction effects of the tested parameters affecting the dextranase activity and stability. The numerical optimization study suggested that the desired maximum activity and stability of dextranase can be obtained at temperature 40 °C and pH value 6.5. In addition, stability tests showed that dextranase was stable, without compromising its activity, up to 55 °C and in pH range 5–8. Considering the influence of investigated reagents on dextranase activity, the results revealed a pronounced activating effect of glycerol and sucrose, especially with increasing their concentration, with the highest activity detected in the presence of sucrose at 10 mM (129%). Regarding the influence of added metal ions, the higher dextranase activity is recorded in the presence of Ag+, Ca2+, K+, Mg2+, and Si2+ions, from which the Ca2+ions were the most effective, and in their presence, at 10 mM the activity of dextranase was 119%.