The COVID-19 pandemic has made it essential to explore alternative antiviral materials. Alginate is a biodegradable, renewable, biocompatible, water-soluble and antiviral biopolymer with many potential biomedical applications. In this regard, this review shows 17 types of viruses that have been tested in contact with alginate and its related biomaterials. Most of these studies show that alginate-based materials possess little or no toxicity and are able to inhibit a wide variety of viruses affecting different organisms: in humans by the human immunodeficiency virus type 1, the hepatitis A, B, and C viruses, Sindbis virus, herpes simplex virus type 1 and 2, poliovirus type 1, rabies virus, rubella virus, and the influenza virus; in mice by the murine norovirus; in bacteria by the T4 coliphage, and in plants by the tobacco mosaic virus and the potato virus X. Many of these are enveloped positive-sense single-stranded RNA viruses, like SARS-CoV-2, which render alginate-based materials highly promising in the COVID-19 pandemic.