This work shows an optimized enzymatic hydrolysis of high molecular weight potato galactan yielding pectic galactan-oligosaccharides (PGOs), where endo-β-1,4-galactanase (galactanase) from Cellvibrio japonicus and Clostridium thermocellum was used. For this, response surface methodology (RSM) by central composite design (CCD) was applied. The parameters varied were temperature (°C), pH, incubation time (min), and enzyme/substrate ratio (U/mg). The optimized conditions for the production of low degree of polymerization (DP) PGOs were obtained for each enzyme by spectrophotometric assay and confirmed by chromatography. The optimal conditions predicted for the use of C. japonicus galactanase to obtain PGOs of DP = 2 were T = 51.8 °C, pH 5, E/S = 0.508 U/mg, and t = 77.5 min. For DP = 3, they were T = 21 °C, pH 9, E/S = 0.484 U/mg, and t = 12.5 min; and for DP = 4, they were T = 21 °C, pH 5, E/S = 0.462 U/mg, and t = 12.5 min. The efficiency results were 51.3% for substrate hydrolysis. C. thermocellum galactanase had a lower yield (35.7%) and optimized conditions predicted for PGOs of DP = 2 were T = 60 °C, pH 5, E/S = 0.525 U/mg, and time = 148 min; DP = 3 were T = 59.7 °C, pH 5, E/S = 0.506 U/mg, and time = 12.5 min; and DP = 4, were T = 34.5 °C, pH 11, E/S = 0.525 U/mg, and time = 222.5 min. Fourier transformed infrared (FT-IR) and nuclear magnetic resonance (NMR) characterizations of PGOs are presented.