Symptoms of the new coronavirus infection that appeared in 2019 (COVID-19) range from low fever and fatigue to acute pneumonia and multiple organ failure. The clinical picture of COVID-19 is heterogeneous and involves most physiological systems; therefore, drugs with a wide spectrum of mechanism of action are required. The choice of the treatment strategy for post-COVID-19 syndrome is still a challenge to be resolved. Polysaccharides with a high fucose content derived from seaweed and marine animals can form the basis for the subsequent development of promising agents for the treatment of COVID-19 and post-COVID-19 syndrome. This class of biopolymers is characterized by a variety of biological activities, including antiviral, antithrombotic, anticoagulant, hemo-stimulating, anti-inflammatory and immune-regulatory. Low molecular weight derivatives of these polysaccharides, as well as synthetic oligosaccharides with a sufficient amount and sulfation type may be considered as the most promising compounds due to their better bioavailability, which undoubtedly increases their therapeutic potential.