Pomegranate (Punica granatumL.) is a rich source of polyphenols, including ellagitannins and ellagic acid. The plant is used in traditional medicine, and its purified components can provide anti-inflammatory and antioxidant activity and support of host defenses during viral infection and recovery from disease. Current data show that pomegranate polyphenol extract and its ellagitannin components and metabolites exert their beneficial effects by controlling immune cell infiltration, regulating the cytokine secretion and reactive oxygen and nitrogen species production, and by modulating the activity of the NFκB pathway. In vitro, pomegranate extracts and ellagitannins interact with and inhibit the infectivity of a range of viruses, including SARS-CoV-2. In silico docking studies show that ellagitannins bind to several SARS-CoV-2 and human proteins, including a number of proteases. This warrants further exploration of polyphenol–viral and polyphenol–host interactions in in vitro and in vivo studies. Pomegranate extracts, ellagitannins and ellagic acid are promising agents to target the SARS-CoV-2 virus and to restrict the host inflammatory response to viral infections, as well as to supplement the depleted host antioxidant levels during the stage of recovery from COVID-19.