Galactose-rich oligosaccharides/oligomers (oligo-RG I) were produced by the enzymatic treatment of potato galactan-rich rhamnogalacturonan I (RG I) with endo-β-1,4-galactanase and Depol 670L multi-enzymatic preparation. The digestibility study revealed that 81.6 and 79.3% of RG I and its corresponding oligomers remained unhydrolyzed, respectively. The prebiotic properties of RG I and its hydrolysates were investigated using a continuous culture system inoculated with immobilized fecal microbiota. Both RG I and oligo-RG I have stimulated the growth of Bifidobacterium spp. and Lactobacillus spp., with oligo-RG I hydrolysates being more selectively fermented by these beneficial bacteria. Furthermore, none of RG I nor its hydrolysates increased the populations of Bacteroidetes and Clostridium leptum. Total amounts of short chain fatty acids, generated upon the fermentation of oligo-RG I, were higher than those obtained with its parent RG I and the positive control (fructooligosaccharides). The overall study contributes to the understandings of the prebiotic properties of potato RG I and its corresponding oligosaccharides/oligomers.