The emergent human coronavirus SARS-CoV-2 and its resistance to current drugs makes the need for new potent treatments for COVID-19 patients strongly necessary. Dextran sulfate (DS) polysaccharides have long demonstrated antiviral activity against different enveloped viruses in vitro. However, their poor bioavailability has led to their abandonment as antiviral candidates. Here, we report for the first time the broad-spectrum antiviral activity of a DS-based extrapolymeric substance produced by the lactic acid bacterium Leuconostoc mesenteroides B512F. Time of addition assays with SARS-CoV-2 pseudoviruses in in vitro models confirm the inhibitory activity of DSs in the early stages of viral infection (viral entry). In addition, this exopolysaccharide substance also reports broad-spectrum antiviral activity against several enveloped viruses such as SARS-CoV-2, HCoV229E, HSV-1, in in vitro models and in human lung tissue. The toxicity and antiviral capacity of DS from L. mesenteroides was tested in vivo in mouse models which are susceptible to SARS-CoV-2 infection. The described DS, administered by inhalation, a new route of administration for these types of polymers, shows strong inhibition of SARS-CoV-2 infection in vivo, significantly reducing animal mortality and morbidity at non-toxic doses. Therefore, we suggest that it may be considered as a potential candidate for antiviral therapy against SARS-CoV-2.