This paper investigates the production and optimization of $eta$-galactosidase enzyme using synthetic medium by Kluyveromyces lactis NRRL Y-8279 in stirred tank bioreactor. Response surface methodology was used to investigate the effects of fermentation parameters on $eta$-galactosidase enzyme production. Maximum specific enzyme activity of 4,622.7 U/g was obtained at the optimum levels of process variables (aeration rate 2.21 vvm, agitation speed 173.4 rpm, initial sugar concentration 33.8 g/L, incubation time 24.0 hr). The optimum temperature and pH of the $eta$-galactosidase enzyme produced under optimized conditions were $37^{circ}C$ and pH 7.0, respectively. The enzyme was stable over a pH range of 6.0-7.5 and a temperature range of $25-37^{circ}C$. The $K_m$ and $V_{max}$ values for O-nitrophenol-$eta$-D-galactopyranoside (ONPG) were 1.20 mM and $1,000;{mu}mol/min{cdot}mg$ protein, respectively. The response surface methodology was found to be useful in optimizing and determining the interactions among process variables in $eta$-galactosidase enzyme production. Hence, this study fulfills the lack of using mathematical and statistical techniques in optimizing the $eta$-galactosidase enzyme production in stirred tank bioreactor.