The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2)-initiated outbreak of COVID-19 has spread rapidly around the world, posing a huge threat to public health. Natural oligo- and polysaccharides with low toxicity, good sustainability, high biocompatibility, respectable safety, immune regulation, and antiviral activity can be employed as promising candidates for the prevention and inhibition of viral infections, especially COVID-19. Glycosaminoglycans, marine polysaccharides, terrestrial plant polysaccharides, and some others have exhibited potential antiviral activity against pathogenic viruses, in the format of polysaccharide-centered vaccine adjuvants, nano-based structures, drug conveyance platforms, etc. In this review, significant recent advancements pertaining to the antiviral applications of oligo- and polysaccharides against SARS-CoV-2 are highlighted, including important challenges and future perspectives.